Laws of Reflection Using Huygens' Principle

Q. You have learnt in the text how Huygens’ principle leads to the lawsof reflection and refraction. Use the same principle to deduce directlythat a point object placed in front of a plane mirror produces avirtual image whose distance from the mirror is equal to the objectdistance from the mirror.

Q. Two transparent media $1$ and $2$ are separated by a plane boundary. The speed of light in medium $1$ is $2.0\times {10}^8{\text{ms}}^{-1}$ and in medium $2$ is $2.5\times {10}^8{\text{ms}}^{-1}$. The critical angle for which a ray of light going from $1$ to $2$ is totally internally reflected is

1. ${\sin }^{-1}\left(\frac{1}{2}\right)$
2. ${\sin }^{-1}\left(\frac{2}{5}\right)$
3. ${\sin }^{-1}\left(\frac{4}{5}\right)$
4. ${\sin }^{-1}\left(\frac{1}{3}\right)$

Q. The wavefront of a light beam is given by the equation $x+2y+3x=c$ (where c is arbitrary constant), then the angle made by the direction of light with the y-axis is

1. $si{n}^{-1}\frac{3}{\sqrt{14}}$
2. $co{s}^{-1}\frac{1}{\sqrt{4}}$
3. $co{s}^{-1}\frac{2}{\sqrt{14}}$
4. $si{n}^{-1}\frac{2}{\sqrt{14}}$

Q. Answer in brief:
Derive the laws of reflection of light using Huygen's principle.

Q. Consider a spherical wavefront incident on a plane mirror. After reflection, we will get,

1. a spherical wavefront
2. a plane wavefront
3. Insufficient information
4. a cylindrical wavefront