A spherical surface of radius of curvature R separates air (refractive index 1.0) from glass (refractive index 1.5). The centre of curvature is in the glass. A point object P placed in air is found to have a real image Q in the glass. The line PQ cuts the surface at a point O, and `PO=OQ`. The distance `PO`

Options

A. 5 R
B. 3 R
C. 2 R
D. `1.5 R`

Answer

A

Explanation

Here, `mu_1 = 1, mu_2 = 1.5`, Let `PO = OQ =x`
As light is travelling from Rerer to Denser medium,
`:. (mu_1)/(-u) + (mu_2)/(v) = (mu_2 - mu_1)/( R)`
`:. (1)/(-(-x)) + (1.5)/(x) = (1.5 - 1)/( R)`
`(1)/(x) + (1.5)/(x) = (0.5)/( R)`
or `(2.5)/(x) = (0.5)/( R)` or `x = 5 R`.