Question

The angle of a prism is ‘A’. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence of 2A on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index, n, of the prism is ______.

Options

• 2 sin A

• 2 cos A

• `1/2 cos A`

• tan A

Answer 1

The refractive index, n, of the prism is 2 cos A.

Explanation:

To retrace its path, a light ray should fall normally on a silvered surface.

Now, it is clear from the geometry of the adjoining figure that,

i = 2A ...(given)

and r = 90° − ∠PTS

= 90° − (90° − A)

= A

Now, by applying Snell’s law the refractive index

n = `sin i/sin r`

= `(sin 2A)/sin A`

= `(2 sin A cos A)/sin A`

= 2 cos A