Refractive Index and Critical Angle

Refractive index (n) is a measure of how light propagates through a medium. It is defined as the ratio of the speed of light in vacuum to the speed of light in the medium. The refractive index of a medium with respect to air (n_air) is given as √2.

Finding the Critical Angle

The critical angle is the angle of incidence at which light is refracted at an angle of 90 degrees with respect to the normal. Beyond this angle, total internal reflection occurs. To find the critical angle, we can use Snell's law, which relates the angle of incidence (θ_1), the angle of refraction (θ_2), and the refractive indices of the two mediums (n_1 and n_2).

Snell's Law
Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two mediums. Mathematically, it can be expressed as:

n_1 * sin(θ_1) = n_2 * sin(θ_2)

In this case, we are considering the refractive index of the medium with respect to air (n_air). Therefore, we can rewrite Snell's law as:

n_air * sin(θ_1) = 1 * sin(θ_2)

Since the refractive index of air is approximately 1, the equation simplifies to:

sin(θ_1) = sin(θ_2)

Critical Angle Condition
The critical angle occurs when the angle of refraction (θ_2) is 90 degrees. Therefore, we have:

sin(θ_1) = sin(90°)
sin(θ_1) = 1

Finding the Critical Angle
To find the critical angle, we need to determine the angle whose sine is equal to 1. In trigonometry, the value of sine is equal to 1 when the angle is 90 degrees. Therefore, the critical angle (θ_c) is equal to 90 degrees.

Summary
The critical angle between two mediums can be found using Snell's law. In this case, where the refractive index of a medium with respect to air is √2, the critical angle is equal to 90 degrees.

45 degree