Engineering Physics by Gaur and Gupta

Explanation: If the angle of incidence in a denser medium equals the critical angle, we are asked to find the corresponding angle of refraction in the rarer medium. This involves understanding how Light bends when crossing boundaries between media with different optical densities.

Refraction occurs when Light changes direction while passing from one medium to another due to a change in speed. The critical angle is defined as the angle of incidence in the denser medium for which the refracted ray in the rarer medium travels along the boundary, making the angle of refraction 90°. Snell’s law relates the angles and refractive indices as: n₁ × sin(θ₁) = n₂ × sin(θ₂).

When the incidence angle equals the critical angle, sin(θ₂) = 1, meaning the refracted ray travels along the interface. Any larger incidence angle results in total internal reflection.

Analogy: It is like pushing a toy car up a ramp — at a certain angle, it reaches the edge exactly, and beyond that, it cannot move forward.

In summary, at the critical angle, Light travels along the boundary, illustrating total internal reflection and the relationship between the incidence angle and refractive index.

Explanation: The absolute refractive index of air indicates how much Light slows down when passing through air compared to vacuum. It measures the optical density of air relative to vacuum, where Light travels fastest.

The absolute refractive index n is calculated as: n = c / v, where c is the speed of Light in vacuum, and v is the speed of Light in the medium. In air, Light slows down very slightly, so n is slightly greater than 1.

The tiny deviation from 1 occurs due to the low density of air molecules. Precise values of n are important in Optics, telescopes, and laser systems.

Analogy: Light moving through air is like a cyclist pedaling through very thin fog — it moves almost freely, but not entirely without resistance.

In summary, air has a refractive index just above 1, showing that Light travels almost as fast as in vacuum, with minimal slowing.

Explanation: The question concerns the refractive index of a material relative to air, which depends on how much light slows down when entering that medium from air. This determines how light bends at the interface.

The refractive index n = c / v, where c is the speed of light in vacuum and v is the speed in the medium. In any medium denser than air, light slows down, so n > 1. Negative or zero values are not physically possible in ordinary transparent materials. The refractive index equals 1 only in vacuum or air.

Example: A light ray entering glass or water from air slows down, bends toward the normal, and the ratio of speeds determines the refractive index. Denser media always have larger refractive indices.

Analogy: Running from a smooth path (air) into mud (medium) slows you down, showing “optical resistance.”

In summary, the refractive index of any normal material relative to air is always greater than 1, meaning light travels slower in the medium than in air.