State Huygen's principle. Using Huygen's wave theory, prove the laws of reflection.

Using Huygen's principle, show that the angle of incidence is equal to the angle of reflection when a plane wavefront is reflected by a plane surface.

A monochromatic light wave is incident normally on a glass slab of thickness $d$, as shown in the figure. The refractive index of the slab increases linearly from $n_1$ to $n_2$ over the height $h$. Which of the following statement(s) is(are) true about the light wave emerging out of the slab?

Calculate the longest wavelength that can be analysed by a rock salt crystal of spacing $\mathrm{d}=2.82 \stackrel{\mathrm{o}}{\mathrm{A}}$ in the first order.

State Huygens' principle.

On a hot summer night, the refractive index of air is the smallest near the ground and increases with a height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light beam,

Deduce  Snell's law of refraction for a plane wave using Huygens' principle.