Question

A point source of light S is placed at the bottom of a vessel containing a liquid of refracting index 5/3. A person is viewing the source from above the surface. there is an opaque disc of radius 2 cm floating on the surface of the liquid such that the center of the disc is vertically above the source S. 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 from above is

• A. 1.33 cm
• B. 2.66 cm
• C. 3.99 cm
• D. 0.33 m

Answer 1

The correct option is A 1.33 cm

$SinC=\frac{r}{\sqrt{r^2+h^2}}$

r = radius of the disk

h = Height of the liquid for both the source can't be seen

$SinC=\frac{1}{\mu }$

$\frac{1}{\mu }=\frac{r}{\sqrt{r^2+h^2}}$

by simplification

$h=r\sqrt{{\mu }^2-1}$

$h=\sqrt{(\frac{5}{3}{)}^2-1}$

$h=\frac{4}{3}cm=1.33cm$

Hence (A) option is correct