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

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:

`(n_(w))/(v) + (n)/(v') = (n - n_(w))/(R)`

`0 + (n)/(2R) = (n - 1.33)/(R)`

Since, v is taken as infinite

n = 2.66