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Question

A concave mirror of focal length 20 cm and a convex lens of focal length 10 cm are kept with their optic axis parallel but separated by 0.5 mm as shown in the figure. The distance between the lens and the mirror is 10 cm. An object of height 3 mm is placed on the optical axis of the lens at a distance of 15 cm from the lens. Find the height of the image (in mm) formed by the mirror after refraction from the lens.

IMAGE

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Solution

We know that: 1v1u=1f

For image formed by mirror:

u1=15 cm

(Direction of incident ray is positive)
For image formed by lens:

1v1115=110

v1=+30 cm

IMAGE

We know that: 1v+1u=1f

For image formed by mirror:

u1=+20 cm

(Direction of incident ray is positive)

For image formed by mirror:

1v2+120=120

v2=10 cm

IMAGE

We know that: M=vu,M=hiho

Overall magnification

M=(v1u1)(v2u2)

M=(3015)(1020)

M=1

Length of image=M×ho

Length of image =(1)(3)=3 mm

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