Question

A transparent thin film of uniform thickness and refractive index $n _{1}=1.4$ is coated on the convex spherical surface of radius $R$ at one end of a long solid glass cylinder of refractive index $n_{2}=1.5$, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance $f _{1}$ from the film, while rays of light traversing from glass to air get focused at distance $f _{2}$ from the film. Then

• A. $| f_1 |=3R$
• B. $| f_1 |=2.8R$
• C. $| f_2 |=2R$
• D. $| f_2 |=1.4R$

Answer 1

Answer: (C)

$| f_2 |=2R$

Answer 2

For air to glass
$\frac{1.5}{f_{1}}=\frac{1.4-1}{R}+\frac{1.5-1.4}{R}$
$\therefore f_{1}=3 \,R$
For glass to air.
$\frac{1}{f_{2}}=\frac{1.4-1.5}{-R}+\frac{1-1.4}{-R}$
$\therefore f_{2}=2\, R$