Visible Light Is a Narrow Slice of a Family That Stretches Far Beyond It
Calculate the deviation produced by a prism and see why violet bends most, place the seven bands of the electromagnetic spectrum in order of wavelength, list the properties every one of them shares, compare infrared with ultraviolet, and explain the blue sky by scattering.
Why does a prism split white light when a windowpane does not?
Send a narrow beam of sunlight through a rectangular sheet of glass and it comes out white, going in the same direction it went in. Send the same beam through a triangular prism and it fans out into a band of colours. Both are the same glass.
The difference is that a prism's two faces are not parallel.
- In a flat sheet, the ray bends one way at the first face and back by the same amount at the second, because the faces are parallel. The two bendings cancel, so all the colours emerge parallel to one another and overlap again into white
- In a prism, the faces are inclined to each other, so the two bendings add instead of cancelling. The ray comes out deviated — and because each colour is deviated by a slightly different amount, the colours separate
That second point is the heart of the chapter. Glass does not have one refractive index; it has a slightly different one for each colour. Violet light is slowed most and bent most; red light is slowed least and bent least. A prism magnifies that tiny difference into a visible spread of colour, and the spread is called dispersion.
And then the chapter widens out. If red and violet are the two ends of what the eye can see, what lies beyond them?
- Beyond red, at longer wavelengths, is infrared — the radiation you feel as warmth from a fire
- Beyond violet, at shorter wavelengths, is ultraviolet — the radiation that tans and burns skin
- And far beyond both lie microwaves, radio waves, X-rays and gamma rays
All of them are the same kind of wave as visible light, differing only in wavelength, and together they form the electromagnetic spectrum. Visible light is a very narrow band inside it.
The part closes with scattering, which explains in one idea why the sky is blue, why a sunset is red, and why danger signals are red rather than green.
This page covers the fourth part of the ICSE Class 10 Physics chapter on light: deviation and dispersion by a prism, the electromagnetic spectrum, infrared and ultraviolet radiation, and the scattering of light.
The difference is that a prism's two faces are not parallel.
- In a flat sheet, the ray bends one way at the first face and back by the same amount at the second, because the faces are parallel. The two bendings cancel, so all the colours emerge parallel to one another and overlap again into white
- In a prism, the faces are inclined to each other, so the two bendings add instead of cancelling. The ray comes out deviated — and because each colour is deviated by a slightly different amount, the colours separate
That second point is the heart of the chapter. Glass does not have one refractive index; it has a slightly different one for each colour. Violet light is slowed most and bent most; red light is slowed least and bent least. A prism magnifies that tiny difference into a visible spread of colour, and the spread is called dispersion.
And then the chapter widens out. If red and violet are the two ends of what the eye can see, what lies beyond them?
- Beyond red, at longer wavelengths, is infrared — the radiation you feel as warmth from a fire
- Beyond violet, at shorter wavelengths, is ultraviolet — the radiation that tans and burns skin
- And far beyond both lie microwaves, radio waves, X-rays and gamma rays
All of them are the same kind of wave as visible light, differing only in wavelength, and together they form the electromagnetic spectrum. Visible light is a very narrow band inside it.
The part closes with scattering, which explains in one idea why the sky is blue, why a sunset is red, and why danger signals are red rather than green.
This page covers the fourth part of the ICSE Class 10 Physics chapter on light: deviation and dispersion by a prism, the electromagnetic spectrum, infrared and ultraviolet radiation, and the scattering of light.
Formula
How do you calculate the deviation produced by a prism?
Add the angle of incidence and the angle of emergence and subtract the angle of the prism.
where is the angle of deviation, the angle of incidence at the first face, the angle of emergence at the second, and the refracting angle of the prism. The two angles of refraction inside the glass satisfy
What the deviation depends on, and a question asks for all four:
- The angle of incidence — the deviation falls to a minimum and then rises again as is increased
- The angle of the prism — a thicker wedge deviates more
- The material of the prism, through its refractive index
- The colour of the light, because the refractive index depends on the wavelength
Minimum deviation. As the angle of incidence is increased from small values, the deviation first decreases, reaches a least value, and then increases again. At that least value the ray passes symmetrically through the prism, so
and the deviation becomes
Worked example 1 — minimum deviation for an equilateral prism. An equilateral prism is made of glass of refractive index . Find the angle of incidence and the deviation at minimum deviation.
At minimum deviation the ray inside the prism runs parallel to the base and
Applying Snell's law at the first face:
The deviation:
Check with the general formula. At minimum deviation , so
The two routes agree, which confirms both the symmetry condition and the arithmetic.
Worked example 2 — a general position. A ray enters an equilateral prism at an angle of incidence of and emerges at . Find the deviation.
And note that this is larger than the minimum for that prism, as it must be — the ray is not passing symmetrically, since .
Worked example 3 — finding the emergence angle. For a prism of refracting angle , a ray is deviated by when the angle of incidence is . Find the angle of emergence.
Now dispersion, which is the same formula applied twice. Because the refractive index of glass is largest for violet and smallest for red:
- Violet is slowed most inside the glass and deviated most
- Red is slowed least and deviated least
- The other colours lie in between, in the order red, orange, yellow, green, blue, indigo, violet
So the band of colours emerging from a prism has red at the top, nearest the incident direction, and violet at the bottom, furthest from it — with the prism's base downward. The band is the visible spectrum, and the colours run in the order remembered as VIBGYOR read from violet to red.
The definition to state precisely. Dispersion is the splitting of white light into its constituent colours on passing through a refracting medium, and it happens because the refractive index of the medium is different for different wavelengths.
Two boundary cases that test whether the reason is understood.
- A glass slab does not produce a visible spectrum, even though it disperses the light inside itself, because its parallel faces bring the colours back out parallel and overlapping
- A second, inverted prism placed after the first recombines the colours into white light, since it deviates each colour back by the same amount the first prism deviated it
And one about speed. All the colours travel at the same speed in vacuum. They differ in speed only inside a material medium, which is why dispersion happens in glass and water but never in empty space.
where is the angle of deviation, the angle of incidence at the first face, the angle of emergence at the second, and the refracting angle of the prism. The two angles of refraction inside the glass satisfy
What the deviation depends on, and a question asks for all four:
- The angle of incidence — the deviation falls to a minimum and then rises again as is increased
- The angle of the prism — a thicker wedge deviates more
- The material of the prism, through its refractive index
- The colour of the light, because the refractive index depends on the wavelength
Minimum deviation. As the angle of incidence is increased from small values, the deviation first decreases, reaches a least value, and then increases again. At that least value the ray passes symmetrically through the prism, so
and the deviation becomes
Worked example 1 — minimum deviation for an equilateral prism. An equilateral prism is made of glass of refractive index . Find the angle of incidence and the deviation at minimum deviation.
At minimum deviation the ray inside the prism runs parallel to the base and
Applying Snell's law at the first face:
The deviation:
Check with the general formula. At minimum deviation , so
The two routes agree, which confirms both the symmetry condition and the arithmetic.
Worked example 2 — a general position. A ray enters an equilateral prism at an angle of incidence of and emerges at . Find the deviation.
And note that this is larger than the minimum for that prism, as it must be — the ray is not passing symmetrically, since .
Worked example 3 — finding the emergence angle. For a prism of refracting angle , a ray is deviated by when the angle of incidence is . Find the angle of emergence.
Now dispersion, which is the same formula applied twice. Because the refractive index of glass is largest for violet and smallest for red:
- Violet is slowed most inside the glass and deviated most
- Red is slowed least and deviated least
- The other colours lie in between, in the order red, orange, yellow, green, blue, indigo, violet
So the band of colours emerging from a prism has red at the top, nearest the incident direction, and violet at the bottom, furthest from it — with the prism's base downward. The band is the visible spectrum, and the colours run in the order remembered as VIBGYOR read from violet to red.
The definition to state precisely. Dispersion is the splitting of white light into its constituent colours on passing through a refracting medium, and it happens because the refractive index of the medium is different for different wavelengths.
Two boundary cases that test whether the reason is understood.
- A glass slab does not produce a visible spectrum, even though it disperses the light inside itself, because its parallel faces bring the colours back out parallel and overlapping
- A second, inverted prism placed after the first recombines the colours into white light, since it deviates each colour back by the same amount the first prism deviated it
And one about speed. All the colours travel at the same speed in vacuum. They differ in speed only inside a material medium, which is why dispersion happens in glass and water but never in empty space.
What is the electromagnetic spectrum, and what do all its members share?
It is the whole family of electromagnetic radiations arranged in order of wavelength, of which visible light is one narrow band.
The seven regions, in order of increasing wavelength, with approximate ranges:
- Gamma rays — shorter than about m. Emitted by radioactive nuclei
- X-rays — about m to m. Produced when fast electrons strike a metal target
- Ultraviolet — about m to m. Emitted by the sun, arcs and mercury vapour lamps
- Visible light — about m to m, which is to angstrom. Violet at the short end, red at the long end
- Infrared — about m to m. Emitted by all hot bodies
- Microwaves — about m to a few tenths of a metre. Produced by special electronic valves
- Radio waves — longer than about a tenth of a metre. Produced by oscillating electric circuits
Read that list backwards and it is in order of increasing frequency and increasing energy, since
means a shorter wavelength goes with a higher frequency. Gamma rays are the most energetic and the most penetrating; radio waves the least.
Notice how narrow visible light is. It spans only a factor of two in wavelength, from about to about angstrom, while the whole spectrum spans many powers of ten. The eye responds to a very small window of what is there, and infrared and ultraviolet lie just outside it on either side.
The properties common to all electromagnetic radiations, which is a standard list question:
- They are all transverse waves, consisting of oscillating electric and magnetic fields at right angles to each other and to the direction of travel
- They all travel through vacuum at the same speed, m s
- They need no material medium for their propagation, so they travel through vacuum
- They are not deflected by electric or magnetic fields, because they carry no charge
- They all obey the laws of reflection and refraction, and show interference, diffraction and polarisation
- They all carry energy, and the energy is greater for a shorter wavelength
- They are all produced by accelerated or oscillating charges
The two properties most often tested are the second and the fourth. All of them travel at the same speed in vacuum — so a radio wave and a gamma ray cross empty space equally fast, and only their wavelengths and frequencies differ. And none of them is deflected by a magnet, which is how electromagnetic radiation is distinguished from a beam of charged particles such as alpha or beta rays.
Worked example — wavelength from frequency. A radio station broadcasts at a frequency of megahertz. Find the wavelength of its waves.
Three metres, which places it firmly in the radio region — and it is why radio aerials are of that order of size.
Worked example 2 — frequency from wavelength. Find the frequency of visible light of wavelength angstrom.
**Compare that with the radio station's Hz and the enormous span of the spectrum becomes concrete: visible light oscillates about a million times faster.
One thing the word "electromagnetic" is telling you. Each of these waves is a travelling disturbance of an electric field and a magnetic field together, each generating the other as the wave advances. That is why no medium is needed** — there is nothing being shaken except the fields themselves, and that is the fundamental difference between electromagnetic waves and sound.
The seven regions, in order of increasing wavelength, with approximate ranges:
- Gamma rays — shorter than about m. Emitted by radioactive nuclei
- X-rays — about m to m. Produced when fast electrons strike a metal target
- Ultraviolet — about m to m. Emitted by the sun, arcs and mercury vapour lamps
- Visible light — about m to m, which is to angstrom. Violet at the short end, red at the long end
- Infrared — about m to m. Emitted by all hot bodies
- Microwaves — about m to a few tenths of a metre. Produced by special electronic valves
- Radio waves — longer than about a tenth of a metre. Produced by oscillating electric circuits
Read that list backwards and it is in order of increasing frequency and increasing energy, since
means a shorter wavelength goes with a higher frequency. Gamma rays are the most energetic and the most penetrating; radio waves the least.
Notice how narrow visible light is. It spans only a factor of two in wavelength, from about to about angstrom, while the whole spectrum spans many powers of ten. The eye responds to a very small window of what is there, and infrared and ultraviolet lie just outside it on either side.
The properties common to all electromagnetic radiations, which is a standard list question:
- They are all transverse waves, consisting of oscillating electric and magnetic fields at right angles to each other and to the direction of travel
- They all travel through vacuum at the same speed, m s
- They need no material medium for their propagation, so they travel through vacuum
- They are not deflected by electric or magnetic fields, because they carry no charge
- They all obey the laws of reflection and refraction, and show interference, diffraction and polarisation
- They all carry energy, and the energy is greater for a shorter wavelength
- They are all produced by accelerated or oscillating charges
The two properties most often tested are the second and the fourth. All of them travel at the same speed in vacuum — so a radio wave and a gamma ray cross empty space equally fast, and only their wavelengths and frequencies differ. And none of them is deflected by a magnet, which is how electromagnetic radiation is distinguished from a beam of charged particles such as alpha or beta rays.
Worked example — wavelength from frequency. A radio station broadcasts at a frequency of megahertz. Find the wavelength of its waves.
Three metres, which places it firmly in the radio region — and it is why radio aerials are of that order of size.
Worked example 2 — frequency from wavelength. Find the frequency of visible light of wavelength angstrom.
**Compare that with the radio station's Hz and the enormous span of the spectrum becomes concrete: visible light oscillates about a million times faster.
One thing the word "electromagnetic" is telling you. Each of these waves is a travelling disturbance of an electric field and a magnetic field together, each generating the other as the wave advances. That is why no medium is needed** — there is nothing being shaken except the fields themselves, and that is the fundamental difference between electromagnetic waves and sound.
What are the properties and uses of infrared and ultraviolet radiation?
Infrared lies just beyond red and is detected as heat; ultraviolet lies just beyond violet and is detected by the chemical and fluorescent effects it causes.
Infrared radiation.
How it is produced and detected. It is emitted by all hot bodies — a fire, a filament lamp, a human body, the sun. It is detected by a blackened thermometer bulb, which shows a rise in temperature, or by a thermopile. Its heating effect is the reason it is sometimes called heat radiation.
Its properties.
- It has a longer wavelength than visible light, so it is scattered less by dust, haze and fog and can travel through them
- It is strongly absorbed by glass and by water, which is why a greenhouse traps it
- It produces a marked heating effect when absorbed
Its uses.
- Heat therapy for muscular pain and sprains, using infrared lamps, because the radiation penetrates below the skin
- Remote controls for televisions and other appliances, which send coded infrared pulses
- Night-vision devices and thermal imaging, which detect the infrared emitted by warm bodies in the dark
- Infrared photography, which can take clear pictures through haze and fog and from great heights
- Greenhouses, where visible light enters through the glass and the infrared re-emitted by the warm soil cannot get out again
- Drying and cooking, as in infrared ovens and grills
Ultraviolet radiation.
How it is produced and detected. It comes from the sun, from electric arcs and from mercury vapour lamps. It is detected by the fluorescence it causes in certain substances, which glow visibly when ultraviolet falls on them, and by its action on a photographic plate.
Its properties.
- It has a shorter wavelength and higher energy than visible light, so it causes chemical changes
- It is absorbed strongly by ordinary glass but passes through quartz, which is why ultraviolet lamps use quartz envelopes
- Most of the sun's ultraviolet is absorbed by the ozone in the upper atmosphere before it reaches the ground
Its uses.
- Sterilising water, air and surgical instruments, because it destroys bacteria
- Detecting forged signatures, currency notes and documents, which is possible because inks fluoresce differently under it
- Producing vitamin D in the skin, which is why some exposure to sunlight is beneficial
- Checking the purity of substances such as ghee, oils and gemstones, by the fluorescence they show
- Producing visible light in a fluorescent tube, where the ultraviolet from the discharge makes the coating on the inside of the tube glow
Its harmful effects, which must be mentioned. In excess, ultraviolet causes sunburn, damages the skin and can lead to skin cancer, and it can cause cataract by damaging the lens of the eye. This is why the depletion of the ozone layer matters — the ozone is what absorbs most of it.
The comparison table in words, which is the answer to "distinguish between infrared and ultraviolet":
- Wavelength: infrared is longer than visible light, ultraviolet shorter
- Energy: ultraviolet carries more energy per photon
- Detection: infrared by its heating effect, ultraviolet by fluorescence and by photographic action
- Effect on glass: infrared is absorbed and trapped, ultraviolet is absorbed but does not warm the glass appreciably
- Effect on the body: infrared warms and soothes, ultraviolet produces vitamin D in small doses and damages tissue in large ones
One thing worth being clear about. Infrared is not "heat" and ultraviolet is not "light". Both are electromagnetic radiation, exactly like visible light, and infrared feels warm only because our skin absorbs it strongly. Visible light absorbed by a black surface warms it just as effectively — the distinction is in what absorbs the radiation, not in the radiation itself.
Infrared radiation.
How it is produced and detected. It is emitted by all hot bodies — a fire, a filament lamp, a human body, the sun. It is detected by a blackened thermometer bulb, which shows a rise in temperature, or by a thermopile. Its heating effect is the reason it is sometimes called heat radiation.
Its properties.
- It has a longer wavelength than visible light, so it is scattered less by dust, haze and fog and can travel through them
- It is strongly absorbed by glass and by water, which is why a greenhouse traps it
- It produces a marked heating effect when absorbed
Its uses.
- Heat therapy for muscular pain and sprains, using infrared lamps, because the radiation penetrates below the skin
- Remote controls for televisions and other appliances, which send coded infrared pulses
- Night-vision devices and thermal imaging, which detect the infrared emitted by warm bodies in the dark
- Infrared photography, which can take clear pictures through haze and fog and from great heights
- Greenhouses, where visible light enters through the glass and the infrared re-emitted by the warm soil cannot get out again
- Drying and cooking, as in infrared ovens and grills
Ultraviolet radiation.
How it is produced and detected. It comes from the sun, from electric arcs and from mercury vapour lamps. It is detected by the fluorescence it causes in certain substances, which glow visibly when ultraviolet falls on them, and by its action on a photographic plate.
Its properties.
- It has a shorter wavelength and higher energy than visible light, so it causes chemical changes
- It is absorbed strongly by ordinary glass but passes through quartz, which is why ultraviolet lamps use quartz envelopes
- Most of the sun's ultraviolet is absorbed by the ozone in the upper atmosphere before it reaches the ground
Its uses.
- Sterilising water, air and surgical instruments, because it destroys bacteria
- Detecting forged signatures, currency notes and documents, which is possible because inks fluoresce differently under it
- Producing vitamin D in the skin, which is why some exposure to sunlight is beneficial
- Checking the purity of substances such as ghee, oils and gemstones, by the fluorescence they show
- Producing visible light in a fluorescent tube, where the ultraviolet from the discharge makes the coating on the inside of the tube glow
Its harmful effects, which must be mentioned. In excess, ultraviolet causes sunburn, damages the skin and can lead to skin cancer, and it can cause cataract by damaging the lens of the eye. This is why the depletion of the ozone layer matters — the ozone is what absorbs most of it.
The comparison table in words, which is the answer to "distinguish between infrared and ultraviolet":
- Wavelength: infrared is longer than visible light, ultraviolet shorter
- Energy: ultraviolet carries more energy per photon
- Detection: infrared by its heating effect, ultraviolet by fluorescence and by photographic action
- Effect on glass: infrared is absorbed and trapped, ultraviolet is absorbed but does not warm the glass appreciably
- Effect on the body: infrared warms and soothes, ultraviolet produces vitamin D in small doses and damages tissue in large ones
One thing worth being clear about. Infrared is not "heat" and ultraviolet is not "light". Both are electromagnetic radiation, exactly like visible light, and infrared feels warm only because our skin absorbs it strongly. Visible light absorbed by a black surface warms it just as effectively — the distinction is in what absorbs the radiation, not in the radiation itself.
Why is the sky blue and the setting sun red?
Because the molecules of the air scatter short wavelengths far more strongly than long ones.
What scattering is. When light passes through a medium containing very small particles — molecules, dust, water droplets — part of it is absorbed by each particle and then re-emitted in all directions. That redirected light is scattered light, and the rest of the beam continues onward, weakened.
The key law, which decides everything in this section. The intensity of the scattered light is inversely proportional to the fourth power of the wavelength:
So a short wavelength is scattered much more strongly than a long one. Violet and blue, at the short end of the visible spectrum, are scattered far more than orange and red at the long end. The fourth power is what makes the effect so pronounced — a modest difference in wavelength becomes a large difference in scattering.
Why the sky is blue. Sunlight entering the atmosphere is scattered by the air molecules.
- The blue and violet components are scattered strongly, in all directions
- Some of that scattered blue light reaches your eye from every part of the sky, even from directions well away from the sun
- So the whole sky glows blue, while the direct beam from the sun, having lost some of its blue, looks slightly yellow
Why not violet, since violet is scattered even more? Because the sun emits less violet than blue, and the eye is much less sensitive to violet — so the mixture we perceive is blue.
Why the sun looks red at sunrise and sunset. At those times the sun is near the horizon, so its light travels through a much longer path of atmosphere to reach you.
- Along that long path almost all the blue has been scattered away sideways out of the beam
- What survives to reach your eye is mainly the long wavelengths — orange and red
- So the sun and the clouds near it appear reddish
At noon the sun is overhead, the path through the atmosphere is at its shortest, comparatively little blue is removed, and the sun appears nearly white.
Why danger signals and brake lights are red. Red has the longest wavelength in the visible spectrum, so it is scattered least by fog, mist and dust and travels the furthest through them without being dispersed.
- A red light remains visible from a great distance in poor weather
- A blue or green light of the same brightness would be scattered away much sooner
- Which is why stop signals, tail lamps and warning lights are red rather than any other colour
Why the sky appears black to an astronaut. Above the atmosphere there are no molecules to scatter sunlight, so no light reaches the eye except directly from the sun and from illuminated objects. The sky is therefore black even in full sunlight, and the stars are visible in the daytime.
Worked reasoning — why clouds are white. Clouds are made of water droplets much larger than the wavelength of light.
- Large particles scatter all wavelengths almost equally, so the fourth-power law no longer applies
- The scattered light therefore contains all the colours in nearly their original proportions, and appears white
- A thick cloud looks grey because much of the light has been scattered away before it can pass through
And that contrast is the boundary case worth stating. The law applies only when the scattering particles are comparable in size to, or smaller than, the wavelength of light — as air molecules are. When they are much larger, as in a cloud or in fog, all colours scatter alike and the result is white or grey. So the same physical process gives a blue sky and a white cloud, and the difference is entirely the size of the particles.
One more everyday case. The sea often looks blue for the same reason the sky does — scattering by the water molecules — and it looks brown or green near a river mouth because larger suspended particles there scatter all colours together.
What scattering is. When light passes through a medium containing very small particles — molecules, dust, water droplets — part of it is absorbed by each particle and then re-emitted in all directions. That redirected light is scattered light, and the rest of the beam continues onward, weakened.
The key law, which decides everything in this section. The intensity of the scattered light is inversely proportional to the fourth power of the wavelength:
So a short wavelength is scattered much more strongly than a long one. Violet and blue, at the short end of the visible spectrum, are scattered far more than orange and red at the long end. The fourth power is what makes the effect so pronounced — a modest difference in wavelength becomes a large difference in scattering.
Why the sky is blue. Sunlight entering the atmosphere is scattered by the air molecules.
- The blue and violet components are scattered strongly, in all directions
- Some of that scattered blue light reaches your eye from every part of the sky, even from directions well away from the sun
- So the whole sky glows blue, while the direct beam from the sun, having lost some of its blue, looks slightly yellow
Why not violet, since violet is scattered even more? Because the sun emits less violet than blue, and the eye is much less sensitive to violet — so the mixture we perceive is blue.
Why the sun looks red at sunrise and sunset. At those times the sun is near the horizon, so its light travels through a much longer path of atmosphere to reach you.
- Along that long path almost all the blue has been scattered away sideways out of the beam
- What survives to reach your eye is mainly the long wavelengths — orange and red
- So the sun and the clouds near it appear reddish
At noon the sun is overhead, the path through the atmosphere is at its shortest, comparatively little blue is removed, and the sun appears nearly white.
Why danger signals and brake lights are red. Red has the longest wavelength in the visible spectrum, so it is scattered least by fog, mist and dust and travels the furthest through them without being dispersed.
- A red light remains visible from a great distance in poor weather
- A blue or green light of the same brightness would be scattered away much sooner
- Which is why stop signals, tail lamps and warning lights are red rather than any other colour
Why the sky appears black to an astronaut. Above the atmosphere there are no molecules to scatter sunlight, so no light reaches the eye except directly from the sun and from illuminated objects. The sky is therefore black even in full sunlight, and the stars are visible in the daytime.
Worked reasoning — why clouds are white. Clouds are made of water droplets much larger than the wavelength of light.
- Large particles scatter all wavelengths almost equally, so the fourth-power law no longer applies
- The scattered light therefore contains all the colours in nearly their original proportions, and appears white
- A thick cloud looks grey because much of the light has been scattered away before it can pass through
And that contrast is the boundary case worth stating. The law applies only when the scattering particles are comparable in size to, or smaller than, the wavelength of light — as air molecules are. When they are much larger, as in a cloud or in fog, all colours scatter alike and the result is white or grey. So the same physical process gives a blue sky and a white cloud, and the difference is entirely the size of the particles.
One more everyday case. The sea often looks blue for the same reason the sky does — scattering by the water molecules — and it looks brown or green near a river mouth because larger suspended particles there scatter all colours together.
Exam tip
Which habits protect the marks in a spectrum or scattering question?
Name the wavelength dependence explicitly whenever you explain a colour effect, and get the spectrum order the right way round.
- **Use ** and , and note that at minimum deviation and
- Say that violet is deviated most and red least, and give the reason — the refractive index is greatest for the shortest wavelength
- Explain why a glass slab gives no spectrum — parallel faces, so the colours emerge parallel and recombine
- List the spectrum in the direction the question asks for, and check the ends: gamma rays at the short-wavelength end, radio waves at the long one
- Remember that all electromagnetic waves travel at the same speed in vacuum and are not deflected by electric or magnetic fields
- Give at least three uses each for infrared and ultraviolet, and one harmful effect of ultraviolet
- **Quote the scattering law as rather than saying "blue scatters more" without a reason
- Say "longer path through the atmosphere" when explaining the red sunset
- Say "no atmosphere to scatter light" when explaining the black sky in space
- State the particle-size condition when asked why clouds are white
The misconception to name. Dispersion is not caused by the prism shape alone, and it does not happen in vacuum. All colours travel at exactly the same speed in vacuum, so no separation can occur there; they separate only inside a medium, where each colour has its own speed and therefore its own refractive index. A prism does not create the colours — they were present in the white light all along, and the prism only spreads them out.
A second trap. Saying the sky is violet because violet has the shortest visible wavelength and is scattered most. The scattering law is right but the conclusion is wrong**, because sunlight contains less violet than blue and the eye is far less sensitive to violet. The correct answer names both facts, and stopping at the scattering law alone loses the mark.
- **Use ** and , and note that at minimum deviation and
- Say that violet is deviated most and red least, and give the reason — the refractive index is greatest for the shortest wavelength
- Explain why a glass slab gives no spectrum — parallel faces, so the colours emerge parallel and recombine
- List the spectrum in the direction the question asks for, and check the ends: gamma rays at the short-wavelength end, radio waves at the long one
- Remember that all electromagnetic waves travel at the same speed in vacuum and are not deflected by electric or magnetic fields
- Give at least three uses each for infrared and ultraviolet, and one harmful effect of ultraviolet
- **Quote the scattering law as rather than saying "blue scatters more" without a reason
- Say "longer path through the atmosphere" when explaining the red sunset
- Say "no atmosphere to scatter light" when explaining the black sky in space
- State the particle-size condition when asked why clouds are white
The misconception to name. Dispersion is not caused by the prism shape alone, and it does not happen in vacuum. All colours travel at exactly the same speed in vacuum, so no separation can occur there; they separate only inside a medium, where each colour has its own speed and therefore its own refractive index. A prism does not create the colours — they were present in the white light all along, and the prism only spreads them out.
A second trap. Saying the sky is violet because violet has the shortest visible wavelength and is scattered most. The scattering law is right but the conclusion is wrong**, because sunlight contains less violet than blue and the eye is far less sensitive to violet. The correct answer names both facts, and stopping at the scattering law alone loses the mark.
Did you know
Why does the same air that makes the sky blue also make sunsets red?
The blue sky and the red sunset are not two effects. They are the two halves of a single one, and you can see them at the same moment.
When the sun is low, look toward it and then away from it.
- Look toward the sun and you are seeing the surviving beam — the light that has come the long way through the atmosphere and lost its blue along the route. It is red
- Look away from the sun and you are seeing the scattered light — precisely the blue that was taken out of that beam. It is blue
Every bit of blue missing from the sun is somewhere in the sky. Nothing has been destroyed; it has only been redirected, and you are standing where you can check both books at once.
Which explains a detail people notice but rarely connect. The reddest sunsets happen when the air carries extra fine particles — after a dusty day, or in smoky conditions — because more scattering means more blue removed from the direct beam. Very clean air gives a paler, yellower sunset.
And the same accounting explains the colour of a distant hill. Mountains far away look bluish, because the air between you and them scatters blue light into your line of sight, laying a faint blue veil over the view. The further the hill, the more air, the bluer it looks — which is why distance in a landscape reads as haze.
The fourth-power law is worth feeling the size of. Since scattering goes as , halving the wavelength multiplies the scattering by sixteen. **Blue light of about angstrom is scattered several times as strongly as red light of about angstrom, purely from that fourth power — and it is the steepness of the power, not the size of the wavelength difference, that makes the sky such a definite colour.
One consequence for photography, which the infrared section already hinted at. Because infrared has a longer wavelength than any visible light, it is scattered still less, so an infrared photograph of a hazy landscape is far clearer than an ordinary one. The same law that blues the sky is what lets an infrared camera see through the haze, and it is why aerial survey photographs are often taken in infrared.
And a last connection to the first section of this page. A rainbow is dispersion and scattering working together: sunlight is refracted on entering a raindrop, totally internally reflected at its back surface, and refracted again on leaving — with each colour deviated by its own amount, exactly as in a prism. So a rainbow is a sky full of tiny prisms, which is why it appears opposite the sun and why red is always on the outside of the arc. Every idea in this part of the chapter is present in a single raindrop.**
When the sun is low, look toward it and then away from it.
- Look toward the sun and you are seeing the surviving beam — the light that has come the long way through the atmosphere and lost its blue along the route. It is red
- Look away from the sun and you are seeing the scattered light — precisely the blue that was taken out of that beam. It is blue
Every bit of blue missing from the sun is somewhere in the sky. Nothing has been destroyed; it has only been redirected, and you are standing where you can check both books at once.
Which explains a detail people notice but rarely connect. The reddest sunsets happen when the air carries extra fine particles — after a dusty day, or in smoky conditions — because more scattering means more blue removed from the direct beam. Very clean air gives a paler, yellower sunset.
And the same accounting explains the colour of a distant hill. Mountains far away look bluish, because the air between you and them scatters blue light into your line of sight, laying a faint blue veil over the view. The further the hill, the more air, the bluer it looks — which is why distance in a landscape reads as haze.
The fourth-power law is worth feeling the size of. Since scattering goes as , halving the wavelength multiplies the scattering by sixteen. **Blue light of about angstrom is scattered several times as strongly as red light of about angstrom, purely from that fourth power — and it is the steepness of the power, not the size of the wavelength difference, that makes the sky such a definite colour.
One consequence for photography, which the infrared section already hinted at. Because infrared has a longer wavelength than any visible light, it is scattered still less, so an infrared photograph of a hazy landscape is far clearer than an ordinary one. The same law that blues the sky is what lets an infrared camera see through the haze, and it is why aerial survey photographs are often taken in infrared.
And a last connection to the first section of this page. A rainbow is dispersion and scattering working together: sunlight is refracted on entering a raindrop, totally internally reflected at its back surface, and refracted again on leaving — with each colour deviated by its own amount, exactly as in a prism. So a rainbow is a sky full of tiny prisms, which is why it appears opposite the sun and why red is always on the outside of the arc. Every idea in this part of the chapter is present in a single raindrop.**
Exam relevance
How are the spectrum and scattering tested in JEE and NEET?
This is foundation work for Class 12 Ray Optics, Electromagnetic Waves and Dual Nature of Radiation, all examined in JEE Main and NEET Physics.
Where the prism formula leads. Class 12 keeps and unchanged, and adds the relation at minimum deviation in the form — which is exactly the calculation you do here in two steps, written as one line. JEE Main sets it as a direct numerical, and also asks for the condition under which a ray fails to emerge from the second face, which is the total-internal-reflection test of the previous part.
Where dispersion leads. Class 12 defines angular dispersion as the difference between the deviations of violet and red, and the dispersive power of the material as that difference divided by the mean deviation. It then builds the achromatic combination, in which two prisms of different materials cancel the dispersion while keeping some deviation. The statement here that a second inverted prism recombines the colours is the starting point of that idea.
Where the spectrum ordering leads. Class 12 Electromagnetic Waves treats the whole spectrum quantitatively, with used constantly and the photon energy introduced in Dual Nature of Radiation. The fact you learn here — that a shorter wavelength carries more energy — becomes that equation, and NEET uses it in every photoelectric-effect question.
Where the common properties lead. The statement that electromagnetic waves are transverse, need no medium, travel at in vacuum and are undeflected by electric and magnetic fields is examined directly in Class 12, often as an assertion-reason item distinguishing them from cathode rays and from alpha and beta particles. That last property is the deciding one, and it is worth being able to state with its reason: the radiation carries no charge.
Where the infrared and ultraviolet material leads. Class 12 discusses the greenhouse effect and the role of ozone quantitatively, and infrared and ultraviolet reappear in Chemistry as spectroscopic tools. NEET Biology uses the ultraviolet material in the discussion of vitamin D and of ozone depletion.
Where scattering leads. Class 12 names it Rayleigh scattering and states the law explicitly, using it for the blue sky, the reddening at sunset and the white cloud. The particle-size condition you note here is what separates Rayleigh scattering from the large-particle case, and questions turn on exactly that distinction.
Question types to expect. At this level: deviation numericals, minimum-deviation conditions, the spectrum in order, properties and uses of infrared and ultraviolet, and colour explanations by scattering. In competitive papers: the minimum-deviation formula for the refractive index, dispersive power, photon energies, and assertion-reason items on electromagnetic wave properties.
The single trap that costs marks. Claiming that dispersion occurs in vacuum. All colours travel at the same speed there, so no separation is possible, and dispersion needs a medium in which the refractive index depends on the wavelength. In Class 12 the same error appears as assuming that a pulse of white light spreads out while crossing empty space, which it does not.
A second trap. Answering "why is the sky blue?" with the scattering law alone. **The full answer needs both the law and the fact that the eye is less sensitive to violet — and both JEE and NEET set the question in a form that rewards the second half.
Board versus competitive emphasis. The ICSE paper marks the labelled prism diagram, the substituted deviation, the ordered spectrum, the listed uses and the reasoned colour explanation; a competitive paper marks a refractive index from a minimum-deviation measurement, or a photon energy. The transferable habit is naming the wavelength dependence in every colour explanation** — because at every level from a blue sky to a photoelectric threshold, the wavelength is the variable that decides the answer.
Where the prism formula leads. Class 12 keeps and unchanged, and adds the relation at minimum deviation in the form — which is exactly the calculation you do here in two steps, written as one line. JEE Main sets it as a direct numerical, and also asks for the condition under which a ray fails to emerge from the second face, which is the total-internal-reflection test of the previous part.
Where dispersion leads. Class 12 defines angular dispersion as the difference between the deviations of violet and red, and the dispersive power of the material as that difference divided by the mean deviation. It then builds the achromatic combination, in which two prisms of different materials cancel the dispersion while keeping some deviation. The statement here that a second inverted prism recombines the colours is the starting point of that idea.
Where the spectrum ordering leads. Class 12 Electromagnetic Waves treats the whole spectrum quantitatively, with used constantly and the photon energy introduced in Dual Nature of Radiation. The fact you learn here — that a shorter wavelength carries more energy — becomes that equation, and NEET uses it in every photoelectric-effect question.
Where the common properties lead. The statement that electromagnetic waves are transverse, need no medium, travel at in vacuum and are undeflected by electric and magnetic fields is examined directly in Class 12, often as an assertion-reason item distinguishing them from cathode rays and from alpha and beta particles. That last property is the deciding one, and it is worth being able to state with its reason: the radiation carries no charge.
Where the infrared and ultraviolet material leads. Class 12 discusses the greenhouse effect and the role of ozone quantitatively, and infrared and ultraviolet reappear in Chemistry as spectroscopic tools. NEET Biology uses the ultraviolet material in the discussion of vitamin D and of ozone depletion.
Where scattering leads. Class 12 names it Rayleigh scattering and states the law explicitly, using it for the blue sky, the reddening at sunset and the white cloud. The particle-size condition you note here is what separates Rayleigh scattering from the large-particle case, and questions turn on exactly that distinction.
Question types to expect. At this level: deviation numericals, minimum-deviation conditions, the spectrum in order, properties and uses of infrared and ultraviolet, and colour explanations by scattering. In competitive papers: the minimum-deviation formula for the refractive index, dispersive power, photon energies, and assertion-reason items on electromagnetic wave properties.
The single trap that costs marks. Claiming that dispersion occurs in vacuum. All colours travel at the same speed there, so no separation is possible, and dispersion needs a medium in which the refractive index depends on the wavelength. In Class 12 the same error appears as assuming that a pulse of white light spreads out while crossing empty space, which it does not.
A second trap. Answering "why is the sky blue?" with the scattering law alone. **The full answer needs both the law and the fact that the eye is less sensitive to violet — and both JEE and NEET set the question in a form that rewards the second half.
Board versus competitive emphasis. The ICSE paper marks the labelled prism diagram, the substituted deviation, the ordered spectrum, the listed uses and the reasoned colour explanation; a competitive paper marks a refractive index from a minimum-deviation measurement, or a photon energy. The transferable habit is naming the wavelength dependence in every colour explanation** — because at every level from a blue sky to a photoelectric threshold, the wavelength is the variable that decides the answer.
Key takeaways
What must you be able to do from this part?
One deviation formula, one spectrum in order, and one fourth-power law.
- A prism deviates light because its faces are not parallel, so the two refractions add instead of cancelling
- ****, with
- Deviation depends on the angle of incidence, the angle of the prism, the material, and the colour of the light
- **At minimum deviation and **, so
- **An equilateral prism of ** has minimum deviation at , with
- Violet has the greatest refractive index and is deviated most; red the least — the spectrum runs red, orange, yellow, green, blue, indigo, violet
- A glass slab gives no spectrum, because its parallel faces let the colours recombine; an inverted second prism recombines them into white light
- All colours travel at the same speed in vacuum, so dispersion cannot happen there
- The spectrum in order of increasing wavelength: gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves, radio waves
- **Visible light spans about to angstrom, violet at the short end and red at the long end
- All electromagnetic radiations** are transverse, need no medium, travel at m s in vacuum, are not deflected by electric or magnetic fields, obey reflection and refraction, and carry more energy at shorter wavelength
- ****, so a MHz radio wave has a wavelength of m, and angstrom light has a frequency of Hz
- Infrared comes from hot bodies, is detected by its heating effect, is scattered little, and is used in heat therapy, remote controls, night vision, haze photography, greenhouses and cooking
- Ultraviolet comes from the sun, arcs and mercury lamps, is detected by fluorescence, is absorbed by glass but passes through quartz, and is used for sterilising, detecting forgery, producing vitamin D, checking purity and lighting fluorescent tubes — and causes sunburn, skin cancer and cataract in excess
- **Scattered intensity , so short wavelengths scatter far more
- The sky is blue because air molecules scatter blue strongly and the eye is less sensitive to violet
- The setting sun is red because the long atmospheric path has scattered the blue away
- Danger signals are red because red is scattered least by fog and travels furthest
- The sky is black in space, with no atmosphere to scatter light
- Clouds are white** because their droplets are much larger than the wavelength and scatter all colours alike
The best self-test costs nothing on a clear evening. Face the setting sun and note its colour, then turn ninety degrees and note the colour of the sky — and say in one sentence why those two colours have to be the two you see.
- A prism deviates light because its faces are not parallel, so the two refractions add instead of cancelling
- ****, with
- Deviation depends on the angle of incidence, the angle of the prism, the material, and the colour of the light
- **At minimum deviation and **, so
- **An equilateral prism of ** has minimum deviation at , with
- Violet has the greatest refractive index and is deviated most; red the least — the spectrum runs red, orange, yellow, green, blue, indigo, violet
- A glass slab gives no spectrum, because its parallel faces let the colours recombine; an inverted second prism recombines them into white light
- All colours travel at the same speed in vacuum, so dispersion cannot happen there
- The spectrum in order of increasing wavelength: gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves, radio waves
- **Visible light spans about to angstrom, violet at the short end and red at the long end
- All electromagnetic radiations** are transverse, need no medium, travel at m s in vacuum, are not deflected by electric or magnetic fields, obey reflection and refraction, and carry more energy at shorter wavelength
- ****, so a MHz radio wave has a wavelength of m, and angstrom light has a frequency of Hz
- Infrared comes from hot bodies, is detected by its heating effect, is scattered little, and is used in heat therapy, remote controls, night vision, haze photography, greenhouses and cooking
- Ultraviolet comes from the sun, arcs and mercury lamps, is detected by fluorescence, is absorbed by glass but passes through quartz, and is used for sterilising, detecting forgery, producing vitamin D, checking purity and lighting fluorescent tubes — and causes sunburn, skin cancer and cataract in excess
- **Scattered intensity , so short wavelengths scatter far more
- The sky is blue because air molecules scatter blue strongly and the eye is less sensitive to violet
- The setting sun is red because the long atmospheric path has scattered the blue away
- Danger signals are red because red is scattered least by fog and travels furthest
- The sky is black in space, with no atmosphere to scatter light
- Clouds are white** because their droplets are much larger than the wavelength and scatter all colours alike
The best self-test costs nothing on a clear evening. Face the setting sun and note its colour, then turn ninety degrees and note the colour of the sky — and say in one sentence why those two colours have to be the two you see.