Question

An observer can see through a pin hole the top end of a thin rod of height h, placed as shown. The beaker height is 3 h and its radius is h. When the beaker is filled with a liquid up to a height 2h ,he can see the lower end of the rod. Then RI of liquid is .

Answer 1

Here is the answer I have attached a png image for the solution

Answer 2

Given :-

Height upto which liquid is filled = 2h

Height of beaker = 3h

Radius of beaker = h

Diameter of beaker = 2h

For refraction from liquid to air.

u = 2h

v = h

As,

tan r = 2h/2h = 1

r = 45°

tan i = h/2h

tan i = 1/2

From this we can find,

Sin i = 1/√5

Sin i/Sin r =$\dfrac{{μ}_{a}}{{μ}_{l}}$

(1/√5)/(1/√2) =$\dfrac{1}{{μ}_{l}}$

$\bf{{μ}_{l}\:=\:\sqrt{\dfrac{5}{2}}}$

Hence,

The refractive index of liquid = μ = √5/2