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: (A), (C)

$|f_1|=3R$
$|f_2|=2R$

Air to glass
$\frac{1.4}{V_1}-\frac{1}{\infty }=\frac{1.4-1}{R}⟶1$
$\frac{1.5}{V}-\frac{1.4}{V_1}=\frac{1.5-1.4}{R}⟶2$
From equation 1 and 2
$\frac{1.5}{f_1}=\frac{0.5}{R}\Rightarrow f_1=3R$
Glass to air
$\frac{1.4}{V_1}-\frac{1.5}{\infty }=\frac{1.4-1.5}{(-R)}=\frac{0.1}{R}⟶3$
$\Rightarrow \frac{1}{V}-\frac{1.4}{V_1}=\frac{1-1.4}{-R}=\frac{0.4}{R}⟶4$
From equation 3 and 4
$\frac{1}{f_2}=\frac{0.5}{R}$
$\therefore f_2=2R$