Question

A point source of light is placed at the bottom of a vessel containing a liquid of Refractive index = 5/3. A person is viewing the source from the above surface. There is an opaque disc of radius 1 cm floating on the surface. The center of the disc lies vertically above the source. The liquid from the vessel is gradually drained out through a tap. The maximum height of the liquid for which the source cannot be seen at all from the above is (in cm):

• A. $\frac{3}{2}$
• B. $\frac{4}{3}$
• C. $\frac{2}{3}$
• D. $\frac{3}{4}$

Answer 1

Answer: (B)

$\frac{4}{3}$

From the definition of critical angle,

tan c $=$ $\frac{r}{h}$

Now, for the given refractive index, tan c $=$ $\frac{1}{\sqrt{{\mu }^2-1}}$

Now, $\mu =\frac{5}{3}$

tan c $=$ $\frac{3}{4}$

Thus,

$\frac{r}{h}=\frac{3}{4}$

For $r=1$

h $=$ $\frac{4}{3}$