8. Thin lensesThin lenses are those whose thickness is small compared to their radius of curvature. They may be either converging or diverging.

Example: An air bubble in a piece of glass has a double convex shape (see below). What type of the lens is formed?

A. Converging B. DivergingC. It depends on

if nin > nout

if nin > nout

1) Types of lenses

1

2) Focus and focal plane

Parallel rays are brought to a focus by a converging lens.

A diverging lens make parallel light diverge.The focal point is that point where the diverging rays would converge if projected back.

2

3) Main equations

fdd i

111

0

o

i

o

i

d

d

h

hm

Thin lens equation Magnification

fP

1Lens power is measured in diopters, D:

111 mD

3

4) Ray tracing (thin converging lenses)f > 0

4

4) Ray tracing (thin diverging lenses) f < 0

The image is upright and virtual

Ray 1 leaves the top of the object and is drawn such that it is parallel to the axis; it emerges from the lens along a line through the focal point on the back side of the lens

Ray 2 leaves the top of the object and is made to pass through the other focal point; it emerges from the lens parallel to the axis.

Ray 3 leaves the top of the object and is directed toward the very center of the lens; it emerges from the lens a the same angle as it entered.

Ray 4 leaves the top of the object and is directed toward 2F on the opposite side of the lens; it emerges from 2F on the same side as the object.

2F2F

4

5

converging lenses

diverging lenses

6

Example 1: The images formed by concave lenses A) are always real B) are always virtual C) could be real or virtual; it depends on whether the object distance is

smaller or greater than the focal lengthD) could be real or virtual, but always real when the object is placed at the

focal point

Example 2: An object is placed between a convex lens and its focal point. The image formed is A) virtual and erect B) virtual and inverted C) real and erectD) real and inverted

Example 3: A convex lens has a focal length f. An object is placed between f and 2f on the axis. The image formed is located A) at 2fB) between f and 2fC) at fD) at a distance greater than 2f from the lens 7

magnification image mirror/lens do di

m<0 inverted, real concave/converging do>f di>f

m>1

0<m<1

upright, virtual concave/converging

convex/diverging

0<do<f

0<do

di<0

-f<di<0

Example: A thin symmetric lens provides an image of a fingerprint with a magnification +0.2 when the fingerprint is 1 cm farther from the lens than the focal point of the lens. What is the type of the image, and what is the type of the lens?

Answer: Image is erect and virtual; this is diverging lenses

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7. Optical instruments

1) Cameras

fdd oi

111 fd 0

There is a certain range of distances over which objects will be in focus; this is called the depth of field of the lens. Objects closer or farther will be blurred.

fdi

oo

i

d

f

d

dm

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2) The Human Eye

The human eye resembles a camera in its basic functioning, with an adjustable lens, the iris, and the retina.

•Most of the refraction is done at the surface of the cornea.

•The lens makes small adjustments to focus at different distances.

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Example: What is the focal length of the eye-lens system when viewing an object a) at infinity, b) 33 cm from the eye? Assume that the lens-retina distance is 2cm.

?

33)

)

2

0

0

f

cmdb

da

cmd ifdd io

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cmfcmcmf

b 9.12

1

33

11 )

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3) Corrective Lenses

a) Nearsightedness can be corrected with a diverging lens

b) And farsightedness with a converging lens

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Vision is blurry underwater because light rays are bent much less than they would be if entering the eye from air.

Near point: closest distance at which eye can focus clearly. Normal NP is about 25 cm.

Far point: farthest distance at which object can be seen clearly. Normal FP is at infinity.

Nearsightedness: far point is too close.

Farsightedness: near point is too far away.

This can be avoided by wearing goggles.

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9. Dispersion in prism

The index of refraction of a material varies somewhat with the wavelength of the light.

This variation in refractive index is why a prism will split visible light into a rainbow of colors.

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Rainbows

Actual rainbows are created by dispersion in tiny drops of water.

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