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. $\left|f_1\right|=3R$
• B. $\left|f_1\right|=2.8R$
• C. $\left|f_2\right|=2R$
• D. $\left|f_2\right|=1.4R$

Answer 1

Answer: (A), (C)

The correct options are
A $\left|f_1\right|=3R$
C $\left|f_2\right|=2R$

For air to glass:

$\Rightarrow \frac{1.5}{f_1}=\frac{1.4-1}{R}+\frac{1.5-1.4}{R}$

$\Rightarrow f_1=3R$
For glass to air:

$\Rightarrow \frac{1}{f_2}=\frac{1.4-1.5}{-R}+\frac{1.14}{-R}$

$\Rightarrow f_2=2R$