A beam of light consisting of red, green, and blue colours is incident on a right-angled prism. The refractive

Question

A beam of light consisting of red, green, and blue colours is incident on a right-angled prism. The refractive index of the material of the prism for the red, green, and blue wavelengths is 1.39, 1.44, and 1.47 respectively. The prism will:

Accepted Answer

1. **Identify Geometry and Incidence:** For a standard right-angled isosceles prism problem where light is incident normally on one leg, it strikes the hypotenuse face at an angle of incidence $i = 45^\circ$.
2. **Condition for Total Internal Reflection (TIR):** TIR occurs at the glass-air interface if the angle of incidence exceeds the critical angle ($i > i_c$).
   $$ \sin i_c = \frac{1}{\mu} $$
   $$ \sin 45^\circ > \frac{1}{\mu} \implies \frac{1}{\sqrt{2}} > \frac{1}{\mu} \implies \mu > \sqrt{2} \approx 1.414 $$
3. **Analyze Each Color:**
   - **Red ($\mu = 1.39$):** Since $1.39 < 1.414$, TIR does not occur. The red light refracts through the hypotenuse.
   - **Green ($\mu = 1.44$):** Since $1.44 > 1.414$, TIR occurs. The green light is totally internally reflected.
   - **Blue ($\mu = 1.47$):** Since $1.47 > 1.414$, TIR occurs. The blue light is totally internally reflected.
4. **Conclusion:** The green and blue components are reflected, while the red component passes through. Thus, the prism separates the red colour from the green and blue colours.

Step-by-Step Solution

Practice All PHYSICS Questions