Given is a thin convex lens of glass (refractive index ) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the o

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Solution

Q.
Given is a thin convex lens of glass (refractive index $μ$ ) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself. [2025]

1 $R / μ$

2 $R / (2 μ - 3)$

3 $μ R$

4 $R / (2 μ - 1)$

Ans.
(4)

$P_{eq} = 2 P_{l} + P_{m} \Rightarrow - \frac{1}{f_{eq}} = \frac{2}{f_{l}} - \frac{1}{f_{m}}$

$- \frac{1}{f_{eq}} = \frac{4 (μ - 1)}{R} - \frac{2}{- R} = \frac{1}{R} (4 μ - 4 + 2)$

$- \frac{1}{f_{eq}} = \frac{1}{R} (4 μ - 2) \Rightarrow \frac{1}{f_{eq}} = \frac{- 1}{R} (4 μ - 2)$

$f_{eq} = \frac{R}{2} \Rightarrow R = 2 f_{eq} = - 2 (\frac{R}{4 μ - 2}) = \frac{- R}{(2 μ - 1)}$

For concave mirror, object should be at 2f for the image to be at same point

Distance = $\frac{R}{(2 μ - 1)}$

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