First slide

Ray optics

Question

AB is a horizontal diameter of a glass sphere of radius R. P is the position of a point object on the extended part of AB at a distance $x$ from A. The image of this object is formed at point Q at a distance $x$ from B. Then refractive index of glass is

Moderate

A

$1 + \frac{x}{R}$
B

$\frac{R}{x}$
C

$\frac{x}{R}$
D

$1 + \frac{R}{x}$

Solution

In this case the refracted ray must be parallel to the diameter AB.
For the refraction at the first surface,
$\frac{μ}{\infty} - \frac{1}{(- x)} = \frac{μ - 1}{(+ R)} \Rightarrow μ = (1 + \frac{R}{x})$

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