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Question

You are given two thin identical plano-convex lenses. When you place an object 20 cm to the left of a single plano-convex lens, the image appears 40 cm to the right of the lens. You then arrange the two plano-convex lenses back to back to form a double convex lens. If the object is at 20 cm to the left of this new lens, what is the approximate location of the image ? Given f=2R for plano-convex lens

A
6.7 cm to the right of the lens
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B
10 cm to the right of the lens
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C
20 cm to the right of the lens
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D
80 cm to the right of the lens
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Solution

The correct option is B 10 cm to the right of the lens
For plano convex lens -
u=20 cm, v=+40 cm, f=2R
1v1u=1f (lens formula)
140+120=12R
R=203
For the convex lens
u=20 cm, f=R=203
Using lens formula,
1v1u=1f
1v+120=320
1v=320120
1v=3120=220
v=10 cm
Why this question?

Concept: 1f=(μ1)(1R11R2) is the formula for finding focal length for all kinds of lenses placed in air.

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