Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B. The separation between the images of O, formed by each refracting surface

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Solution

Q.

Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B. The separation between the images of O, formed by each refracting surface is: [2025]

1 0.214 R

2 0.114 R

3 0.411 R

4 0.124 R

Ans.
(2)

For B

$\frac{μ_{2}}{V_{B}} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R}$

$\frac{1.5}{V_{B}} + \frac{2}{R} = \frac{0.5}{- R}$

$\frac{1.5}{V_{B}} = - \frac{1}{2 R} - \frac{2}{R}$

$\frac{1.5}{V_{B}} = \frac{- 5}{2 R} \Rightarrow V_{B} = - 0.6 R$

For A

$\frac{1.5}{V_{A}} + \frac{2}{3 R} = \frac{0.5}{- R}$

$\frac{1.5}{V_{A}} = - \frac{1}{2 R} - \frac{2}{3 R}$

$\frac{1.5}{V_{A}} = - \frac{7}{6 R} \Rightarrow V_{A} = - \frac{9}{7} R$

Distance between images $= 2 R - (0.6 R + \frac{9}{7} R) = 0.114 R$

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