Reflection and Refraction of Plane Wave at Plane Surface Using Huygens' Principle - Refraction of a Plane Wave

In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index 'n'. For incident angle 60° at the side AC, the refracted light just grazes along face AC. The refractive index of the liquid n = `sqrtx/4`. The value of x is ______.

(Given refractive index of glass = 1.5)

The optical properties of a medium are governed by the relative permittivity (ε_r) and relative permeability (µ_r). The refractive index is defined as `sqrt(µ_r ε_r) = n`. For ordinary material ε_r > 0 and µ_r > 0 and the positive sign is taken for the square root. In 1964, a Russian scientist V. Veselago postulated the existence of material with ε_r < 0 and µ_r < 0. Since then such ‘metamaterials’ have been produced in the laboratories and their optical properties studied. For such materials `n = - sqrt(µ_r ε_r)`. As light enters a medium of such refractive index the phases travel away from the direction of propagation.

1. According to the description above show that if rays of light enter such a medium from air (refractive index = 1) at an angle θ in 2^nd quadrant, them the refracted beam is in the 3^rd quadrant.
2. Prove that Snell’s law holds for such a medium.

Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

The wavefronts of light coming from a distant source of unknown shape are nearly _________ .

Let us list some of the factors, which could possibly influence the speed of wave propagation:

(i) Nature of the source

(ii) Direction of propagation

(iii) Motion of the source and/or observer

(iv) Wavelength

(v) Intensity of the wave

On which of these factors, if any, does the speed of light in vacuum?

A plane wavefront propagating in a medium of refractive index 'μ₁' is incident on a plane surface making the angle of incidence 'i' as shown in the figure. It enters into a medium of refractive index 'μ₂' (μ₂ > μ₁). Use Huygens' construction of secondary wavelets to trace the propagation of the refracted wavefront. Hence verify Snell's law of refraction.

The refractive index of glass is 1.5. What is the speed of light in glass? (Speed of light in vacuum is 3.0 × 10⁸ m s⁻¹)

A light ray in a medium (RI = 5/3) enters another medium at an angle of 30°. The angle in the other medium is sin^-1 (5/6). The incident angle must be increased such that the ray is completely reflected at minimum degrees is ______.