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 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 a distance $f_1$ from the film, while rays of light traversing from glass to air get focused at a 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: (A), (C)

$|f_2|=2R$

For air to glass,
$\frac{1.5}{f_1}=\frac{1.4-1}{R}+\frac{1.5-1.4}{R}\Rightarrow f_1=3R$
For glass to air,
$\frac{1}{f_2}=\frac{1.4-1.5}{-R}+\frac{1-1.4}{-R}\Rightarrow f_2=2R.$
Hence, the correct options are (a) and (c).