Two Lenses Touching Behave Like One With Their Powers Added
Draw ray diagrams for convex and concave lenses, apply the lens formula with the right signs, work out the power of a lens in dioptres and the net power of a combination, and choose the lens an application needs.
Why can two thin lenses replace one thick one?
An optician testing your eyes does not carry a lens for every possible prescription. A small box of standard lenses is enough, because lenses placed in contact simply add up.
where each is the power of a lens — a single number that says how strongly it bends light. A dioptre lens next to a dioptre lens behaves exactly like one dioptre lens, and a next to a behaves like a flat piece of glass.
That addition rule is convenient, but it is also a clue about what a lens actually is: a device whose effect is measured by one number, so that two of them can be combined by arithmetic rather than by redesign.
But before powers can be added, the lens's basic behaviour has to be predictable — which needs three ray rules and one formula, both closely related to the mirror versions from Part 2. A convex lens converges light, like a concave mirror; a concave lens diverges it, like a convex mirror. The sign conventions are the same, and only two details of the formulas differ.
This page covers the third part of the CBSE Class 10 Science chapter on light: ray diagrams for lenses, the lens formula with its sign convention, the power of a lens and of a combination, and choosing between a mirror and a lens for a given job.
where each is the power of a lens — a single number that says how strongly it bends light. A dioptre lens next to a dioptre lens behaves exactly like one dioptre lens, and a next to a behaves like a flat piece of glass.
That addition rule is convenient, but it is also a clue about what a lens actually is: a device whose effect is measured by one number, so that two of them can be combined by arithmetic rather than by redesign.
But before powers can be added, the lens's basic behaviour has to be predictable — which needs three ray rules and one formula, both closely related to the mirror versions from Part 2. A convex lens converges light, like a concave mirror; a concave lens diverges it, like a convex mirror. The sign conventions are the same, and only two details of the formulas differ.
This page covers the third part of the CBSE Class 10 Science chapter on light: ray diagrams for lenses, the lens formula with its sign convention, the power of a lens and of a combination, and choosing between a mirror and a lens for a given job.
How do you draw a ray diagram for a lens?
Three rules, and any two of them locate the image.
- A ray parallel to the principal axis passes, after refraction, through the principal focus of a convex lens — or appears to come from the focus of a concave lens
- A ray passing through the principal focus emerges parallel to the principal axis
- A ray through the optical centre passes straight on without any deviation
That third rule has no counterpart in mirrors and it is the easiest of the three to draw, so it is worth using in almost every diagram.
A convex lens gives six results, exactly parallel to the concave mirror's six:
- Object at infinity — image at the focus on the far side, real, inverted, a point
- **Object beyond ** — image between and , real, inverted, diminished
- **Object at ** — image at , real, inverted, same size
- **Object between and ** — image beyond , real, inverted, enlarged
- **Object at — image at infinity
- Object between and the optical centre — image on the same side as the object, virtual, erect, enlarged
A concave lens gives one result, always. Whatever the object position, the image is between the focus and the optical centre, on the same side as the object, and it is virtual, erect and diminished.
Where the image forms tells you which lens it is. A real image from a lens is on the opposite side from the object, because the light has passed through. A mirror's real image is on the same side, because the light came back. That difference is the single most useful thing to remember when comparing the two.
Worked prediction.** A convex lens of focal length cm has an object cm away. What image do you expect?
Here is at cm, and cm is beyond it, so the image is real, inverted and diminished, lying between and on the far side — that is, between cm and cm from the lens. The next section's formula should give a value in that range, which makes the prediction a check on the arithmetic.
The two boundary cases to be careful about. With the object exactly at the emergent rays are parallel and no image forms at a finite distance — the projector arrangement run backwards. With the object exactly at the image is the same size, which is the case a photocopier uses when copying at full size. Both are rows of the table, and naming F or 2F in a question is usually a pointer to one of them.
- A ray parallel to the principal axis passes, after refraction, through the principal focus of a convex lens — or appears to come from the focus of a concave lens
- A ray passing through the principal focus emerges parallel to the principal axis
- A ray through the optical centre passes straight on without any deviation
That third rule has no counterpart in mirrors and it is the easiest of the three to draw, so it is worth using in almost every diagram.
A convex lens gives six results, exactly parallel to the concave mirror's six:
- Object at infinity — image at the focus on the far side, real, inverted, a point
- **Object beyond ** — image between and , real, inverted, diminished
- **Object at ** — image at , real, inverted, same size
- **Object between and ** — image beyond , real, inverted, enlarged
- **Object at — image at infinity
- Object between and the optical centre — image on the same side as the object, virtual, erect, enlarged
A concave lens gives one result, always. Whatever the object position, the image is between the focus and the optical centre, on the same side as the object, and it is virtual, erect and diminished.
Where the image forms tells you which lens it is. A real image from a lens is on the opposite side from the object, because the light has passed through. A mirror's real image is on the same side, because the light came back. That difference is the single most useful thing to remember when comparing the two.
Worked prediction.** A convex lens of focal length cm has an object cm away. What image do you expect?
Here is at cm, and cm is beyond it, so the image is real, inverted and diminished, lying between and on the far side — that is, between cm and cm from the lens. The next section's formula should give a value in that range, which makes the prediction a check on the arithmetic.
The two boundary cases to be careful about. With the object exactly at the emergent rays are parallel and no image forms at a finite distance — the projector arrangement run backwards. With the object exactly at the image is the same size, which is the case a photocopier uses when copying at full size. Both are rows of the table, and naming F or 2F in a question is usually a pointer to one of them.
Formula
What is the lens formula, and how does it differ from the mirror formula?
Same convention, one sign changed in each of the two equations.
Compare them with the mirror versions, which were and :
- The lens formula has a minus where the mirror formula has a plus
- The lens magnification has no minus sign where the mirror magnification has one
The sign convention itself is unchanged. The object is on the left, distances are measured from the optical centre, rightward is positive, upward is positive. So:
- ** is always negative
- A convex lens has positive ; a concave lens has negative
- A real image has positive , because it forms on the right, beyond the lens
- A virtual image has negative , because it appears on the same side as the object
Notice that the meaning of the sign of has flipped from mirrors.** For a mirror, negative meant real; for a lens, positive means real. That is because light passes through a lens and comes back from a mirror, and it is the commonest source of error in the whole chapter.
Worked example 1 — a real image. An object is placed cm from a convex lens of focal length cm. Find the image position and the magnification.
**Positive means real and on the far side; negative means inverted, twice the size. Check against the table**: cm lies between at cm and at cm, so the image should be real, inverted, enlarged and beyond — and cm is indeed beyond cm. Table and formula agree.
Worked example 2 — a magnifying glass. The same lens with the object only cm away.
**Negative means virtual and on the same side; positive means erect, twice the size. That is exactly how a magnifying glass is used — the object must be closer than the focus.
Worked example 3 — a concave lens.** An object is cm from a concave lens of focal length cm.
Virtual, erect and diminished, about a third of the size and closer to the lens than the object is — the one and only concave-lens case.
The checks to run every time.
- A concave lens can never give a real image, so must come out negative
- A real image from a lens is always inverted, so positive must come with negative
- ** means enlarged
If a concave lens has produced a positive , the arithmetic is wrong** — and that single check catches most sign slips.
Compare them with the mirror versions, which were and :
- The lens formula has a minus where the mirror formula has a plus
- The lens magnification has no minus sign where the mirror magnification has one
The sign convention itself is unchanged. The object is on the left, distances are measured from the optical centre, rightward is positive, upward is positive. So:
- ** is always negative
- A convex lens has positive ; a concave lens has negative
- A real image has positive , because it forms on the right, beyond the lens
- A virtual image has negative , because it appears on the same side as the object
Notice that the meaning of the sign of has flipped from mirrors.** For a mirror, negative meant real; for a lens, positive means real. That is because light passes through a lens and comes back from a mirror, and it is the commonest source of error in the whole chapter.
Worked example 1 — a real image. An object is placed cm from a convex lens of focal length cm. Find the image position and the magnification.
**Positive means real and on the far side; negative means inverted, twice the size. Check against the table**: cm lies between at cm and at cm, so the image should be real, inverted, enlarged and beyond — and cm is indeed beyond cm. Table and formula agree.
Worked example 2 — a magnifying glass. The same lens with the object only cm away.
**Negative means virtual and on the same side; positive means erect, twice the size. That is exactly how a magnifying glass is used — the object must be closer than the focus.
Worked example 3 — a concave lens.** An object is cm from a concave lens of focal length cm.
Virtual, erect and diminished, about a third of the size and closer to the lens than the object is — the one and only concave-lens case.
The checks to run every time.
- A concave lens can never give a real image, so must come out negative
- A real image from a lens is always inverted, so positive must come with negative
- ** means enlarged
If a concave lens has produced a positive , the arithmetic is wrong** — and that single check catches most sign slips.
How do you calculate the power of a lens and of a combination?
Power is the reciprocal of the focal length in metres, and powers of lenses in contact simply add.
The unit is the dioptre, written D, and one dioptre is the power of a lens whose focal length is one metre. A convex lens has positive power and a concave lens negative power, following the sign of .
Worked example 1. Find the power of a convex lens of focal length cm.
The conversion to metres is compulsory. Using would give D, which is a hundred times too small — and forgetting it is the single most common error in power questions.
Worked example 2. Find the power of a concave lens of focal length cm.
Worked example 3 — working backwards. A lens has a power of D. Find its focal length.
Worked example 4 — a combination. A convex lens of power D is placed in contact with a concave lens of power D. Find the net power and the focal length of the combination.
Worked example 5 — two convex lenses. Powers D and D in contact:
Notice that adding lenses makes the focal length shorter, not longer. Power and focal length are reciprocals, so more power means a stronger bend and a nearer focus — which is why a thick, strongly curved lens has a short focal length and a high power.
Worked example 6 — the combination that does nothing. A D lens in contact with a D lens gives
A power of zero means an infinite focal length, so the pair behaves like a flat sheet of glass: light passes through undeviated. The two lenses have not stopped working — they are cancelling each other, which is the clearest demonstration that power is a signed quantity.
Why an optician can work with a small box of lenses. Because any prescription can be built by adding a few standard powers, and the patient reports which combination is clearest. The optician is doing the addition rule in front of you, and the number written on the prescription is the total.
The unit is the dioptre, written D, and one dioptre is the power of a lens whose focal length is one metre. A convex lens has positive power and a concave lens negative power, following the sign of .
Worked example 1. Find the power of a convex lens of focal length cm.
The conversion to metres is compulsory. Using would give D, which is a hundred times too small — and forgetting it is the single most common error in power questions.
Worked example 2. Find the power of a concave lens of focal length cm.
Worked example 3 — working backwards. A lens has a power of D. Find its focal length.
Worked example 4 — a combination. A convex lens of power D is placed in contact with a concave lens of power D. Find the net power and the focal length of the combination.
Worked example 5 — two convex lenses. Powers D and D in contact:
Notice that adding lenses makes the focal length shorter, not longer. Power and focal length are reciprocals, so more power means a stronger bend and a nearer focus — which is why a thick, strongly curved lens has a short focal length and a high power.
Worked example 6 — the combination that does nothing. A D lens in contact with a D lens gives
A power of zero means an infinite focal length, so the pair behaves like a flat sheet of glass: light passes through undeviated. The two lenses have not stopped working — they are cancelling each other, which is the clearest demonstration that power is a signed quantity.
Why an optician can work with a small box of lenses. Because any prescription can be built by adding a few standard powers, and the patient reports which combination is clearest. The optician is doing the addition rule in front of you, and the number written on the prescription is the total.
When should you use a mirror and when a lens?
Use a mirror when the light must come back and a lens when it must go through. Everything else follows from that.
The comparison, point by point.
- Mechanism — a mirror reflects; a lens refracts
- Where a real image forms — in front of a mirror, on the same side as the object; on the far side of a lens
- **Sign of for a real image — negative for a mirror, positive for a lens
- Formula** — for a mirror; for a lens
- Magnification — for a mirror; for a lens
- Converging member — the concave mirror and the convex lens
- Diverging member — the convex mirror and the concave lens
The pairing in those last two lines is worth staring at. Concave is converging for a mirror and diverging for a lens, and convex is the reverse. The words describe the shape, not the effect, and reading them as though they described the effect is a guaranteed error.
Which lens does which job.
- A magnifying glass — a convex lens with the object inside its focus, giving a virtual, erect, enlarged image
- A camera — a convex lens with the object well beyond , giving a real, inverted, diminished image on the film or sensor
- A projector — a convex lens with the object between and , giving a real, inverted, enlarged image on the screen. The slide is put in upside down so that the picture appears the right way up
- Spectacles for a short-sighted eye — a concave lens, of negative power
- Spectacles for a long-sighted eye — a convex lens, of positive power
- A door peephole — a concave lens, giving a wide view of a diminished erect image, the lens equivalent of a convex mirror
Worked selection. Which lens and which object position would you choose to throw a large image of a small slide onto a wall?
A large real image requires a convex lens with the object **between and — the projector row. And it must be real, because a virtual image cannot fall on a wall. The choice is made from the table, not from memory of the device.
One misconception worth clearing. A magnifying glass does not work by being held anywhere near the object at random. It must be closer to the object than its focal length, which is why you have to move it in and out until the image is right — you are hunting for the boundary at F. Move it too far and the image flips over**, because you have crossed into the real-image rows of the table.
The comparison, point by point.
- Mechanism — a mirror reflects; a lens refracts
- Where a real image forms — in front of a mirror, on the same side as the object; on the far side of a lens
- **Sign of for a real image — negative for a mirror, positive for a lens
- Formula** — for a mirror; for a lens
- Magnification — for a mirror; for a lens
- Converging member — the concave mirror and the convex lens
- Diverging member — the convex mirror and the concave lens
The pairing in those last two lines is worth staring at. Concave is converging for a mirror and diverging for a lens, and convex is the reverse. The words describe the shape, not the effect, and reading them as though they described the effect is a guaranteed error.
Which lens does which job.
- A magnifying glass — a convex lens with the object inside its focus, giving a virtual, erect, enlarged image
- A camera — a convex lens with the object well beyond , giving a real, inverted, diminished image on the film or sensor
- A projector — a convex lens with the object between and , giving a real, inverted, enlarged image on the screen. The slide is put in upside down so that the picture appears the right way up
- Spectacles for a short-sighted eye — a concave lens, of negative power
- Spectacles for a long-sighted eye — a convex lens, of positive power
- A door peephole — a concave lens, giving a wide view of a diminished erect image, the lens equivalent of a convex mirror
Worked selection. Which lens and which object position would you choose to throw a large image of a small slide onto a wall?
A large real image requires a convex lens with the object **between and — the projector row. And it must be real, because a virtual image cannot fall on a wall. The choice is made from the table, not from memory of the device.
One misconception worth clearing. A magnifying glass does not work by being held anywhere near the object at random. It must be closer to the object than its focal length, which is why you have to move it in and out until the image is right — you are hunting for the boundary at F. Move it too far and the image flips over**, because you have crossed into the real-image rows of the table.
Exam tip
What layout keeps a lens numerical safe?
Write the signed values, name the lens type, use the correct formula, and interpret the answer in words. The lens formula and the mirror formula differ by one sign each, so naming which you are using is the first defence.
- **Write lens formula or mirror formula before the equation. Mixing the two is the error this whole chapter is designed to expose
- Remember is negative, convex positive, concave negative
- For a lens, positive means real; for a mirror, negative means real. Write the interpretation out
- Use for lenses with no minus sign
- Convert the focal length to metres before finding the power, and give the answer in dioptres
- Add powers with their signs in a combination, and convert back to a focal length at the end
- Check against the six-case table: a concave lens can never give a real image, and a real lens image is always inverted
- State nature, position and size in every image answer
The misconception to name.** Concave and convex describe the shape, not the effect. A concave mirror converges; a concave lens diverges. A question giving you a converging lens is giving you a convex one, and translating the word into the effect before starting is what prevents an entire question from going wrong.
- **Write lens formula or mirror formula before the equation. Mixing the two is the error this whole chapter is designed to expose
- Remember is negative, convex positive, concave negative
- For a lens, positive means real; for a mirror, negative means real. Write the interpretation out
- Use for lenses with no minus sign
- Convert the focal length to metres before finding the power, and give the answer in dioptres
- Add powers with their signs in a combination, and convert back to a focal length at the end
- Check against the six-case table: a concave lens can never give a real image, and a real lens image is always inverted
- State nature, position and size in every image answer
The misconception to name.** Concave and convex describe the shape, not the effect. A concave mirror converges; a concave lens diverges. A question giving you a converging lens is giving you a convex one, and translating the word into the effect before starting is what prevents an entire question from going wrong.
Did you know
Why does a lens of +2 D and one of -2 D together act like plain glass?
Take a convex lens that focuses light at half a metre and a concave lens that spreads it as though from half a metre away, and press them together. Light now goes straight through as if neither were there.
An infinite focal length means no bending at all. The first lens converges the beam by exactly as much as the second diverges it, so the two effects cancel and the emerging rays are parallel to the incident ones — which is what a flat sheet of glass does.
The two lenses have not switched off. Each is bending the light as much as ever; the second is simply undoing the first. Put a piece of paper between them and each lens's effect becomes visible again, which shows that the cancellation happens only because they act in sequence on the same beam.
Opticians use the same arithmetic in the other direction. A prescription of D is assembled from standard lenses in the trial frame, and the patient chooses the clearest combination. The number on your spectacles is the total power of the glass, which is why two people with the same prescription can have lenses of very different thicknesses — the material and the curvature can differ as long as the total comes out right.
And the cancellation trick has a serious use. Real lenses do not focus every colour at the same point, because the refractive index differs slightly for red and violet light — the dispersion you will meet in the next chapter. Combining a converging lens of one glass with a diverging lens of another can cancel that colour spreading while leaving some net power behind, and that is how a good camera or telescope lens is built: several elements whose unwanted effects cancel and whose wanted effects add.
One observation you can make yourself. Look through a pair of spectacles at arm's length and move it about. A short-sighted person's lenses make everything look smaller and a long-sighted person's make it look larger — negative power against positive power, visible without any measurement. And the edge thickness gives it away too: a concave lens is thin in the middle and thick at the rim, and a convex lens is the reverse.
An infinite focal length means no bending at all. The first lens converges the beam by exactly as much as the second diverges it, so the two effects cancel and the emerging rays are parallel to the incident ones — which is what a flat sheet of glass does.
The two lenses have not switched off. Each is bending the light as much as ever; the second is simply undoing the first. Put a piece of paper between them and each lens's effect becomes visible again, which shows that the cancellation happens only because they act in sequence on the same beam.
Opticians use the same arithmetic in the other direction. A prescription of D is assembled from standard lenses in the trial frame, and the patient chooses the clearest combination. The number on your spectacles is the total power of the glass, which is why two people with the same prescription can have lenses of very different thicknesses — the material and the curvature can differ as long as the total comes out right.
And the cancellation trick has a serious use. Real lenses do not focus every colour at the same point, because the refractive index differs slightly for red and violet light — the dispersion you will meet in the next chapter. Combining a converging lens of one glass with a diverging lens of another can cancel that colour spreading while leaving some net power behind, and that is how a good camera or telescope lens is built: several elements whose unwanted effects cancel and whose wanted effects add.
One observation you can make yourself. Look through a pair of spectacles at arm's length and move it about. A short-sighted person's lenses make everything look smaller and a long-sighted person's make it look larger — negative power against positive power, visible without any measurement. And the edge thickness gives it away too: a concave lens is thin in the middle and thick at the rim, and a convex lens is the reverse.
Exam relevance
How are lens numericals set in JEE and NEET?
This is foundation work whose formulas are used unchanged in Class 11 and in both competitive papers.
Where the lens formula leads. Class 11 Ray Optics derives it from refraction at two spherical surfaces, giving the lens maker's formula in terms of the two radii of curvature and the refractive index. The sign convention and the working formula are exactly the ones you use here, and JEE Main sets problems where a lens is immersed in a liquid, so that the refractive index — and therefore the power — changes.
Where the power addition leads. Class 11 extends to lenses separated by a distance, where an extra term appears, and then to the design of optical instruments — the microscope and the telescope, whose magnification is calculated from the powers of the objective and eyepiece. The contact case you learn here is the starting point of all of it.
Where the mirror-lens comparison leads. JEE Advanced problems routinely combine a mirror and a lens, with the image from one becoming the object for the next. Every such problem depends on knowing which side a real image forms on for each element, which is exactly the comparison in this chapter. A sign convention applied to the wrong element ruins the whole chain.
Where the applications lead. The camera, the projector and the magnifying glass reappear as worked instruments, and the eye's own lens is treated in the next chapter — where the power of a corrective lens is calculated with the formula you have just used.
Question types to expect. At this level: lens-formula numericals, power and combination calculations, and choosing a lens for an application. In competitive papers: multi-element problems, lens-in-liquid problems, and assertion-reason items on concave against convex behaviour.
The single trap that costs marks. Using the mirror formula for a lens or the other way round. The lens formula has a minus and the mirror formula a plus, and for a lens against for a mirror. Writing the wrong one gives a plausible number and a wrong answer, which is exactly what a multiple-choice paper is built to catch.
A second trap. Forgetting to convert the focal length to metres before computing power. A focal length in centimetres gives a power a hundred times too small, and in a spectacle-prescription question the answer will look absurd — which is a useful warning if you notice it.
Board versus competitive emphasis. The CBSE paper marks the signed values, the named formula, the substitution and the interpretation; a competitive paper marks the number. The transferable asset is the six-case table plus the two-line comparison with mirrors — between them they predict every answer before you calculate it.
Where the lens formula leads. Class 11 Ray Optics derives it from refraction at two spherical surfaces, giving the lens maker's formula in terms of the two radii of curvature and the refractive index. The sign convention and the working formula are exactly the ones you use here, and JEE Main sets problems where a lens is immersed in a liquid, so that the refractive index — and therefore the power — changes.
Where the power addition leads. Class 11 extends to lenses separated by a distance, where an extra term appears, and then to the design of optical instruments — the microscope and the telescope, whose magnification is calculated from the powers of the objective and eyepiece. The contact case you learn here is the starting point of all of it.
Where the mirror-lens comparison leads. JEE Advanced problems routinely combine a mirror and a lens, with the image from one becoming the object for the next. Every such problem depends on knowing which side a real image forms on for each element, which is exactly the comparison in this chapter. A sign convention applied to the wrong element ruins the whole chain.
Where the applications lead. The camera, the projector and the magnifying glass reappear as worked instruments, and the eye's own lens is treated in the next chapter — where the power of a corrective lens is calculated with the formula you have just used.
Question types to expect. At this level: lens-formula numericals, power and combination calculations, and choosing a lens for an application. In competitive papers: multi-element problems, lens-in-liquid problems, and assertion-reason items on concave against convex behaviour.
The single trap that costs marks. Using the mirror formula for a lens or the other way round. The lens formula has a minus and the mirror formula a plus, and for a lens against for a mirror. Writing the wrong one gives a plausible number and a wrong answer, which is exactly what a multiple-choice paper is built to catch.
A second trap. Forgetting to convert the focal length to metres before computing power. A focal length in centimetres gives a power a hundred times too small, and in a spectacle-prescription question the answer will look absurd — which is a useful warning if you notice it.
Board versus competitive emphasis. The CBSE paper marks the signed values, the named formula, the substitution and the interpretation; a competitive paper marks the number. The transferable asset is the six-case table plus the two-line comparison with mirrors — between them they predict every answer before you calculate it.
Key takeaways
What should you know about lenses before the human eye?
Three ray rules, one formula, one unit and one comparison.
- Three ray rules: parallel goes through F, through F comes out parallel, and through the optical centre goes straight on
- A convex lens gives real inverted images for objects beyond F, the same size at , and a virtual erect enlarged image only inside F
- A concave lens always gives a virtual, erect, diminished image on the same side as the object
- Lens formula , and magnification with no minus sign
- ** negative; convex positive; concave negative
- For a lens, positive means real and on the far side — the opposite of the mirror rule
- Power** , measured in dioptres; convex positive, concave negative
- Convert to metres first — a focal length of cm gives D
- Powers of lenses in contact add, and more power means a shorter focal length
- A mirror reflects and a lens refracts; concave converges for a mirror and diverges for a lens
- Convex lens for a magnifying glass, camera, projector and long sight; concave lens for short sight and a peephole
The sharpest self-test is the pair of convex cases. Take cm with the object first at cm and then at cm, work both out, and check that one gives a real inverted image on the far side and the other a virtual erect one on the near side.
- Three ray rules: parallel goes through F, through F comes out parallel, and through the optical centre goes straight on
- A convex lens gives real inverted images for objects beyond F, the same size at , and a virtual erect enlarged image only inside F
- A concave lens always gives a virtual, erect, diminished image on the same side as the object
- Lens formula , and magnification with no minus sign
- ** negative; convex positive; concave negative
- For a lens, positive means real and on the far side — the opposite of the mirror rule
- Power** , measured in dioptres; convex positive, concave negative
- Convert to metres first — a focal length of cm gives D
- Powers of lenses in contact add, and more power means a shorter focal length
- A mirror reflects and a lens refracts; concave converges for a mirror and diverges for a lens
- Convex lens for a magnifying glass, camera, projector and long sight; concave lens for short sight and a peephole
The sharpest self-test is the pair of convex cases. Take cm with the object first at cm and then at cm, work both out, and check that one gives a real inverted image on the far side and the other a virtual erect one on the near side.