CBSE Class 12 · 2017 · Geometrical OpticsShort Answer

A small illuminated bulb is at the bottom of a tank containing a liquid of refractive index

μ

up to a height

H

. Find the expression for the diameter of an opaque disc, floating symmetrically on the liquid surface, in order to cut off the light from the bulb.

Answer: Diameter $d = \frac{2 H}{μ ^{2} - 1}$ .

Solution

Light can escape only within a cone of semi-vertical angle equal to the critical angle

i_{c}

(

sin i_{c} = 1/ μ

). The disc must cover the circle where this cone meets the surface.

tan i_{c} = \frac{r}{H} \Rightarrow r = H tan i_{c} = H \frac{sin i _{c}}{cos i _{c}} = H \frac{1/ μ}{1 - 1/ μ ^{2}} = \frac{H}{μ ^{2} - 1}

d = 2 r = \frac{2 H}{μ ^{2} - 1}

CBSE Class 12 Board · 2017 · Subjective