Question

What must be 'n' of a sphere surrounded by water so that the parallel rays that affect one of its faces converge on the second vertex of the sphere?

Answer 1

Answer:

The refractive index of the sphere is 2.66

Solution:

The refractive index, $n_{w} = 1.33$ and since the sphere is surrounded by water.

Therefore, according to the question, the parallel rays that affect one of the faces of the sphere converges on the second vortex:

Thus the image distance from the pole  of surface 1, v' = 2R

where

R = Radius of the sphere

Now, using the eqn:

$\frac{n_{w}}{v} + \frac{n}{v'} = \frac{n - n_{w}}{R}$

$0 + \frac{n}{2R} = \frac{n - 1.33}{R}$

Since, v is taken as infinite

n = 2.66