Animated Solution for Physics - Optics: The speed of light in the medium is

If you look at this question and feel like you are missing a piece of the puzzle, you are absolutely right! This question was originally part of a comprehension passage in the AIEEE 2010 exam.

The passage introduced a fascinating concept from non-linear optics: the refractive index of the medium is not constant. Instead, it depends on the intensity of the light passing through it. The relationship given was: where $I$ is the intensity of the light, and ${\mu }_0$ and $c$ are positive constants.

Imagine a laser beam propagating through this medium. Where is the beam the brightest? Naturally, the intensity $I$ is maximum right at the central axis of the beam and gradually fades out as you move towards the edges.

Because the refractive index $\mu$ is directly proportional to the intensity $I$, the medium responds dynamically to the light. At the central axis, where the light is most intense, the refractive index reaches its maximum value. In simple terms, the medium becomes optically denser at the center compared to the edges!

Now, let's bring in the fundamental relationship between the speed of light $v$ and the refractive index $\mu$:

Substituting our expression for the refractive index, we get:

This equation tells a beautiful story. The speed of light $v$ is inversely proportional to the refractive index $\mu$.

Since the refractive index $\mu$ is maximum on the axis of the beam, the denominator in our speed equation is at its largest. Consequently, the speed of light $v$ must dip to its minimum value right on the axis!

It is as if the light is wading through thick honey at the center of the beam while traveling faster at the edges. Therefore, the speed of light is minimum on the axis of the beam.

A Note on the Answer Key: The source material incorrectly lists option (c) as the answer. However, based on rigorous physical deduction, the correct answer is undeniably option (a).