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Question

# The focal length of a lens and mirror are 10 cm and 20 cm respectively. Find the position of the final image.

A
10 cm behind the concave mirror
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B
20 cm in front of concave mirror
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C
20 cm behind the concave mirror
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D
10 cm in front of concave mirror
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Solution

## The correct option is C 20 cm behind the concave mirrorGiven: The distance of object from the convex lens, u=−20 cm Height of image, h=5 cm Focal length of convex lens, f1=10 cm. Focal length of concave mirror, f2=−20 cm (Assuming new cartesian sign convention) Distance between the mirror and the lens, d=30 cm By lens formula, 1f=1v−1u 110=1v−1−20 cm v=20 cm The positive sign show that the image is formed to the right side of the lens. The image v in front of concave mirror, between pole and focus acts as an object for the concave mirror. Hence, the object distance from concave mirror, u′=−10 cm By mirror formula, 1f2=1v′+1u′ 1−20=1v′+1−10 v′=20 cm The image formed by concave mirror is 20 cm behind the mirror.

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