Animated Solution for Physics - Optics: Three rays of light, namely red (R), green (G) and blue (B) are incident on the face PQ of a right angled prism PQR as shown in figure The refractive indices of the material of the prism for red, green and blue wavelength are 1.27, 1.42 and 1.49, respectively. The colour of the ray(s) emerging out of the face PR is

Imagine you are standing in front of a glass prism, shining three distinct laser beams—Red, Green, and Blue—directly at its face. Because you are aiming them perfectly perpendicular to the surface, they don't bend at all upon entering. They march straight through the glass, completely undeviated, until they hit the second boundary: the slanted face of the prism.

Now, let's look at the geometry. The prism is a right-angled triangle, and we know the base angle is $45^{\circ }$. By simple geometry, the normal (the perpendicular line) to the slanted face also makes a $45^{\circ }$ angle with our horizontal laser beams. This means that for all three colors, the angle of incidence $i$ at the second face is exactly $45^{\circ }$.

Here is where the magic of physics takes over. Will the light escape the prism, or will it be trapped inside? This is governed by the phenomenon of Total Internal Reflection (TIR).

For a light ray to be trapped and reflect internally, its angle of incidence must be greater than a specific threshold called the critical angle $i_C$. Mathematically, this condition is written as:

We also know from Snell's Law that the critical angle is related to the refractive index $\mu$ of the material by the equation $\sin i_C=\frac{1}{\mu }$. Substituting this into our inequality, we get the master condition for TIR:

Let's plug in our angle of incidence, $i=45^{\circ }$, to find the threshold refractive index required to trap the light.

This number, 1.414, is our gatekeeper. Any color of light that experiences a refractive index greater than 1.414 will be trapped inside the prism. Let's evaluate our three contenders:

1. Blue Light: ${\mu }_B=1.49$. Since $1.49>1.414$, the blue ray suffers Total Internal Reflection. 2. Green Light: ${\mu }_G=1.42$. Since $1.42>1.414$, the green ray also suffers Total Internal Reflection. 3. Red Light: ${\mu }_R=1.27$. Since $1.27<1.414$, the red ray does not suffer TIR.

Therefore, the red ray is the only one that successfully refracts and emerges out of the prism's slanted face. It's a beautiful demonstration of how a material interacts differently with different wavelengths of light!