Question

ray of light is falling on a glass sphere of refractive index = √3
 such that the incident ray and the emergent ray, when produced, intersect at a point on the surface of the sphere. The value of angle of incidence in degrees is 10x, then x = ?​

Answer 1

Answer:

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Answer 2

x = 6

Explanation:

Please refer to the attached picture for the diagram.

We find that ∠ABC = π − 2 (i − r)

So the external ∠AOC will be 2π − (π-2r) = π + 2r

According to circle property, we know that 2∠ABC = ∠AOC

So 2 [π − 2 (i − r)] =  π + 2r

2i - r = π/2

Hence r = 2i - π/2

μ = sin i / sin r

As μ = √3 is given, we get:

√3 = sin i / sin r

√3 = sin i / sin (2i - π/2)

√3 = sin i / -cos 2i

√3 = sin i / 2sin² i - 1

2√3sin² i  - √3 = sin i

Solving the equation 2√3sin² i  - sin i - √3 = 0, we get:

sin i = √3/2

Which implies that i is 60∘

So 10x = 60∘. Therefore x = 6