Compound LensCompound Lens

Two LensesTwo Lenses A single convex lens produces A single convex lens produces

a real image.a real image. That image can be acted on by That image can be acted on by

a second lens.a second lens.• Second image can be real or Second image can be real or

virtualvirtual

Final ImageFinal Image Two thin convex lenses with Two thin convex lenses with

focal lengths 0.30 m and 0.50 focal lengths 0.30 m and 0.50 m are separated by 0.20 m.m are separated by 0.20 m.

An object is placed 0.50 m in An object is placed 0.50 m in front of the first lens.front of the first lens.

Find the image in the second Find the image in the second lens.lens.

First apply the lens equation to First apply the lens equation to the first lens.the first lens.• ff11 = 0.30 m, = 0.30 m, ssoo11 = 0.50 m = 0.50 m

The intermediate image is The intermediate image is ssoo22 = =

0.75 – 0.20 = 0.55 m beyond 0.75 – 0.20 = 0.55 m beyond the second lens.the second lens.• ff22 = 0.50 m, = 0.50 m, ssoo22 = -0.55 m = -0.55 m

• This is a real imageThis is a real image

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Touching LensesTouching Lenses

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Two lenses are often brought Two lenses are often brought into close contact.into close contact.• Very short distance between Very short distance between

optical centersoptical centers

The combined focal length can The combined focal length can be approximated.be approximated.• Let Let ssoo11 approach infinity approach infinity

• Applies to convex and Applies to convex and concave lensesconcave lenses

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FarsightedFarsighted Some eyes have weak Some eyes have weak

muscles.muscles.• Near image focuses in front of Near image focuses in front of

the retinathe retina

• Hyperopia and presbyopiaHyperopia and presbyopia

A compound converging lens A compound converging lens compensates for the eye’s compensates for the eye’s lens.lens.• Forces the image forward in Forces the image forward in

the eye. the eye.

NearsightedNearsighted Some eyes have eyes too long Some eyes have eyes too long

or bent corneas.or bent corneas.• Distant image focuses in front Distant image focuses in front

of the retinaof the retina

• MyopiaMyopia

A compound diverging lens A compound diverging lens forces the image back in the forces the image back in the eye.eye.• Pinhole iris or squinting also Pinhole iris or squinting also

works works

DioptersDiopters

Optometrics works on corrective lenses for eyes.Optometrics works on corrective lenses for eyes.

Diopters measure the inverse of the focal length of the Diopters measure the inverse of the focal length of the lens.lens.• 1 D = 1 m1 D = 1 m-1-1

• Positive convergingPositive converging• Negative diverging Negative diverging

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Reading GlassesReading Glasses A person sees blurred print at A person sees blurred print at

25 cm, but is fine at 125 cm.25 cm, but is fine at 125 cm. Find the diopter correction Find the diopter correction

needed.needed.

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The diopter formula can be The diopter formula can be applied to object and image applied to object and image distances.distances.• Object is at 0.25 mObject is at 0.25 m

• Virtual image is at 1.25 mVirtual image is at 1.25 m

• Correction needed is +3.2 DCorrection needed is +3.2 D

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