Question

Two monochromatic rays of light are incident normally on the face AB of an isosceles right-angled prism ABC. The refractive indices of the glass prism for the two rays ‘1’ and ‘2’ are respectively 1.35 and 1.45. Trace the path of these rays after entering through the prism.

Answer 1

At plane AC, the incident angle for ray 1 and ray 2 = 45º

Let critical angle for total internal reflection for ray 1 = C₁

_{1.35 = \(\frac{1}{sin\,C_1}⇒sin C_1=\frac{1}{1.35}=0.74\)}

hence C₁ > 45º (sin 45 = 0.707)

Let critical angle for total internal reflection for ray 2 = C₂

1.45 = \(\frac{1}{sin\,C_2}⇒sin C_2 =\frac{1}{1.45}=0.689\)

hence C₂ < 45º (sin 45 = 0.707)

As in case of ray 1, incident angle is less than critical angle, it would emerge out form AC. In figure, the path of the ray 1 is shown.

In case of ray 2, incident angle is greater than critical angle, it would get total internal reflection at AC and emerge from BC.

In the figure, path of the ray 2 is shown