Question

A narrow beam of light of diameter D is inclined on a glass sphere of refractive index $\mu =\frac{3}{2}$ and radius R (D << R). Distance of point from center C of sphere where this beam converges is

• A. R
• B. $\frac{3R}{2}$
• C. $\frac{5R}{2}$
• D. 2R

Answer 1

The correct option is B $\frac{3R}{2}$


For 1st refraction $\Rightarrow \frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

$\frac{\mu }{v_1}-\frac{1}{-\infty }=\frac{\mu -1}{R}$

$\Rightarrow v_1=3R$

For 2nd refraction $\Rightarrow \frac{1}{v_f}-\frac{\mu }{R}=\frac{1-\mu }{-R}$

$v_f=\frac{R}{2}\Rightarrow$ So distance from C is $\frac{3}{2}R$