Rotating the Mirror

Q. Find the angle by which the mirror must be rotated such that the reflected ray will be travelling along the vertical (dotted line) as shown in the figure.
[CW - clockwise, CCW - counter-clockwise]

1. ${105}^{\circ }CCW$
2. ${75}^{\circ }CCW$
3. ${210}^{\circ }CW$
4. ${15}^{\circ }CCW$

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

Q. A small plane mirror placed at the centre of a spherical screen of radius R. A beam of light is falling on the mirror. If the mirror makes n revolution. per second, the speed of light on the screen after reflection from the mirror will be

1. 4ΠnR
2. 2ΠnR
3. 
4. 

Q.

In an attempt to kill Batman , Joker devises another evil Plan.

He mounts a plane mirror AB on a turn table both of which are centered at O.
Around it he places a Death Laser on a ring shaped turn table which is concentric to the other turn table.
Both the tables can turn in either direction. Laser is fixed such that it always points at O.
He knows that to kill Batman he has to turn the ring turn table by 20 degrees more, in the anticlockwise direction, from the given situation in the picture. Fortunately the ring turning mechanism is jammed . So calculate the angle and the direction by which he has to turn the central turn table from the initial position in order to hit Batman.

1. 20 degrees, clockwise
2. 20 degrees, anticlockwise
3. 10 degrees, clockwise
4. 10 degrees, anticlockwise

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 light ray $I$ is incident on a plane mirror $M$. The mirror is rotated in the direction as shown in the figure by an arrow at frequency $\frac{9}{\pi }\text{rps}$. The light reflected by the mirror is received on the wall W at a distance 10 m from the axis of rotation. When the angle of incidence becomes ${37}^{\circ }$, the speed of the spot (a point) on the wall is

1. 10 m/s
2. 1000 m/s
3. 500 m/s
4. None of these

Q. A rotating mirror with uniform angular speed $\omega$ is placed at the centre $\left(C\right)$ of the sphere of radius $\left(R\right)$ as shown in the figure. Incident light falls on the mirror. The linear speed $\left(v\right)$ of the light spot on the sphere is

1. $2\omega R$
2. $3\omega R$
3. $5\omega R$
4. $\omega R$

Q. Images of an object that is equidistant from the two plane mirrors whose reflecting surfaces make an angle of ${90}^{\circ }$ with one another lie on a/an

1. straight line
2. parabola
3. ellipse
4. circle

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. $12$
4. $11$

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. $\theta \ge {60}^{\circ }$