Light from a distant source enters a 0.5 dioptre lens parallel to the optical ax

Question

Light from a distant source enters a 0.5 dioptre lens parallel to the optical axis. (a) How far from the first lens must a second, 1.2 D lens be placed such that the light leaving the second lens is also parallel to the optical axis? (b) How far from the first lens must a second, - 1.5 D lens be placed such that the light leaving the second lens is also parallel to the optical axis? (c) A second 1.2 D lens is placed 1.2 m behind the first. Is the light leaving this lens, converging, diverging, or parallel to the optical axis?

Explanation / Answer

30.8

a)

P1 = power of first lens = 0.5

f1 = focal length of first lens = 100/P1 = 100/0.5 = 200 cm

do = object distance = infinite

di = image distance

using the equation

1/f1 = 1/di + 1/do

1/200 = 1/di + 1/infinite

di = 200 cm

image is formed on the other side of lens at its focus.

for the second lens :

P2 = power of first lens = 1.2

f2 = focal length of first lens = 100/P2 = 100/1.2 = 83.3 cm

for the image by second lens to be at infinity , the object must be at its focus.

so distance between the lenses = f1 + f2 = 200 + 83.3 = 283.3 cm

b)

P1 = power of first lens = 0.5

f1 = focal length of first lens = 100/P1 = 100/0.5 = 200 cm

do = object distance = infinite

di = image distance

using the equation

1/f1 = 1/di + 1/do

1/200 = 1/di + 1/infinite

di = 200 cm

image is formed on the other side of lens at its focus.

for the second lens :

P2 = power of first lens = 1.5

f2 = focal length of first lens = 100/P2 = 100/1.5 = - 66.7 cm

for the image by second lens to be at infinity , the object must be at its focus.

so distance between the lenses = f1 + f2 = 200 - 66.7 = 133.3 cm

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