Rotating the Mirror

Q. A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance $x$ from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle $\theta$, the spot of the light is found to move through a distance $y$ on the scale. The angle $\theta$ is given by

1. $$\frac{x}{y}$$
2. $$\frac{y}{2x}$$
3. $$\frac{y}{x}$$
4. $$\frac{x}{2y}$$

Q. A ray of light makes an angle of ${10}^{\circ }$ with the horizontal above it and strikes a plane mirror which is inclined at an angle $\theta$ to the horizontal. The angle $\theta$ for which the reflected ray becomes vertical is

1. ${40}^{\circ }$
2. ${50}^{\circ }$
3. ${80}^{\circ }$
4. ${100}^{\circ }$

Q. Assertion: If the angle between the two plane mirrors is ${72}^{\circ }$ and the object is asymmetrically placed between the two mirrors, then $5$ images of the object will be formed.
Reason: For a given system of mirrors, the total number of images formed due to successive reflection of an asymmetrically placed object is equal to either $\frac{{360}^{\circ }}{\theta }$ or $\frac{{360}^{\circ }}{\theta }-1$ accordingly as $\frac{{360}^{\circ }}{\theta }$ is odd or even respectively.

1. Both assertion and reason are correct and reason is the correct explanation of assertion.
2. Both assertion and reason are correct and reason is not the correct explanation of assertion.
3. Assertion is correct, but reason is incorrect.
4. Both assertion and reason are incorrect.

Q. A light source lies at the angle bisector of two plane mirrors inclined at an angle of $\theta$. The limitation for the value of $\theta$ so that the light reflected from one mirror does not reach the other mirror will be

1. $\theta \le {120}^{\circ }$
2. $\theta \le {90}^{\circ }$
3. $\theta \ge {120}^{\circ }$
4. $\theta \ge {60}^{\circ }$

Q. Two mirrors placed at an angle of $\theta$ produces $5$ images of an object placed symmetrically between the mirrors. The number of images produced when $\theta$ is decreased by ${30}^{\circ }$ will be

1. $14$
2. $13$
3. $11$
4. $12$

Q.

A plane mirror reflecting a ray of incident light is rotated through an angle about an axis through the point of incidence in the plane of the mirror perpendicular to the plane of incidence, then

1. The reflected ray does not rotate

2. The reflected ray rotates through an angle

3. The reflected ray rotates through an angle

4. The incident ray is fixed