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 centre 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 cm

Answer 1

The correct option is A 1.33 cm

In the given figure,

$A$ is a point source of light. and $EA$ is depth of disc.

Suppose,

$h=$ Depth of water

Angle $EAB=C$

So,

$tanC=\frac{EB}{EA}=\frac{1}{h}$

Now,

When source can not seen at all means all light reflected back that is angle of incidence is critical angle.

$sinC=\frac{1}{n}=\frac{3}{5}$ (Given $n=\frac{5}{3}$)

So,

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

Thus,

$\frac{1}{h}=\frac{3}{4}$

or

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