Question

(i) If the angle of incidence and angle of emergence of a light ray falling on a glass slab are i and e respectively, prove that, i = e.

Answer 1

In the fig SR || PQ and OM is the reflected ray Hence r₁=r₂

Let μ be the refractive index of the glass slab.

Then, according to Snell's law,

Then, according to Snell's law,

\(\frac{sin\,\,i}{sin\,\, r_1}\) = μ .....(i)

and

\(\frac{sin\,\,r_2}{sin\,\, e}\) = \(\frac{1}{μ}\) .... .....(ii)

But r₁=r₂

Putting (iii) in (i), we get

\(\frac{sin\,\,i}{sin\,\, r_2}\) = μ .....(iv)

Multiplying (ii) and (iv), we have

\(\frac{sin\,\,i}{sin\,\, r_2}\) x \(\frac{sin\,\,r_2}{sin\,\, e}\) = μ x \(\frac{1}{μ}\)

∴ \(\frac{sin\,\,i}{sin\,\, e}\) = 1

∴ i = e proved