Derive the law of reflection using Huygens’ wave theory.

On the basis of Huygens’ wave theory show that when light is incident on a plane mirror obliquely, angle of reflection is equal to angle of incidence.

Derive Snell’s law of refraction using Huygens’ wave theory.

State Huygens’ principle. Use it to derive Snell’s law of refraction for a parallel beam incident on the plane surface of a refracting medium. Give proper diagram.

If ‘$\mathrm{d}$’ is the distance travelled by a light-wave in air in ‘$\mathrm{t}$’ seconds and ‘$\mathrm{D}$’ is the distance travelled in a medium of refractive index ‘$\mathrm{n}$’ in the same time, prove that $\mathrm{d}=\mathrm{nD}$.

On the basis of Huygens’ wave theory prove Snell’s law of refraction of light. Draw a neat and labelled diagram. (Postulates of Huygens’ wave theory not required.)

Define optical path and prove that optical path $\left(\mathrm{\Delta }\right)=\mathrm{nd}$, where $\mathrm{n}$ is the refractive index of medium other than the air and ‘$\mathrm{d}$’ is the distance travelled in the medium. If a mica sheet of thickness ‘$\mathrm{t}$’ and refractive index ‘$\mathrm{n}$’ is placed in the path of a ray of light, by how much the optical path is included?

Define wavefront. Which kind of wavefront is produced by a line source of light? Prove law of refraction on the basis of Huygens’ wave theory.

Find the frequency (in megahertz) of radio waves of wavelength $30 \mathrm{m}$.