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

Q. A plane mirror makes an angle of 30 degree with the horizontal.If a vertical ray strikes the mirror, find the angle between mirror and reflected ra

Q. A small object is placed $50cm$ to the left of a thin convex lens of focal length $30cm$ . A convex spherical mirror of radius of curvature $100cm$ is placed to the right of the lens at a distance of $50cm$. The mirror is titled such that the axis of the mirror is at a angle $\theta ={30}^{\circ }$ to the axis of the lens, as shown in the figure.
If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates $\left(incm\right)$ of the point $(x,y)$ at which the image is formed are

1. $(125/3,25/\sqrt{3})$
2. $(50-25\sqrt{3},25)$
3. $(0,0)$
4. $(25,25\sqrt{3})$

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 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 concave mirror has radius of curvature of $40\text{cm}$. It is at the bottom of a glass that has water filled up to $5\text{cm}$
(see figure)
If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d in cm from the surface of water. The value of d is close to

[Refractive index of water = 4/3]

Q. An object is placed symmetrically between two plane mirrors inclined at an angle of ${72}^{\circ }$, then the total number of images observed will be

1. $5$
2. $4$
3. $3$
4. $2$

Q.

How many images of an object are formed if two adjacent walls and the ceiling of a rectangular room are mirror surfaced?

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.

How many images of himself can an observer see if two adjacent walls and the ceiling of a rectangular room are mirror surfaced?

1. $2$

2. $3$

3. $5$

4. $7$

Q. A transparent cylinder has its right half polished so as to act as a mirror. A paraxial light ray incident from left, that is parallel to the pricipal axis, exits parallel to the incident ray as shown. The refractive index $n$ of the material of the cylinder is

1. $1.2$
2. $1.5$
3. $1.8$
4. $2.0$

Q. A plane mirror revolves as shown at constant angular velocity 2rps about its normal. With what velocity will light spot move along spherical screen of radius 10m if mirror is at centre of curvature of screen and light is incident from fixed direction

Q. A glass hemisphere of refractive index $4/3$ and radius $4\text{cm}$ is placed on a plane mirror. A point object is placed at distance ${}^{\prime }{d}^{\prime }$ on the axis of this sphere as shown. If the final image is at infinity, then the value of ${}^{\prime }{d}^{\prime }$ in $\text{cm}$ is

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 ray of light makes an angle 10 degree with horizontal above it and strikes a plane mirror inclined at an angle theta for which reflected ray becomes vertical

Q. The speed at which the image of a luminous point object is moving, if the luminous point object is moving at speed $v_0$ towards a spherical mirror, along its axis is:
(Given, $R=$ radius of curvature & $u=$ object distance)

1. $v_i=-v_0$
2. $v_i=-v_0{\left[\frac{R}{2u-R}\right]}^2$
3. $v_i=-v_0\left[\frac{2u-R}{R}\right]$
4. $v_i=-v_0\left[\frac{R}{2u-R}\right]$

Q. In the figure shown a point object $O$ is placed in air on the principal axis. The radius of curvature of the spherical surface is $60\text{cm}$. $I_f$ is the final image formed after all the refractions and reflections.

1. If $d_1=120\text{cm}$, then the ${}^{\prime }{I}_f^{\prime }$ is formed on ${}^{\prime }{O}^{\prime }$ for any value of $d_2$.
2. If $d_1=240\text{cm}$, then the ${}^{\prime }{I}_f^{\prime }$ is formed on ${}^{\prime }{O}^{\prime }$ only if $d_2=360\text{cm}$.
3. If $d_1=240\text{cm}$, then the ${}^{\prime }{I}_f^{\prime }$ is formed on ${}^{\prime }{O}^{\prime }$ for all values of $d_2$.
4. If $d_1=240\text{cm}$, then the ${}^{\prime }{I}_f^{\prime }$ cannot be formed on ${}^{\prime }{O}^{\prime }$.

Q. In the figure shown, find the angle $\left(\theta \right)$ by which mirror should be rotated. So that the ray of light retraces its path after reflection from mirror $M$.

1. $\theta =2^{\circ }$ anticlockwise
2. $\theta =1^{\circ }$ clockwise
3. $\theta ={3.5}^{\circ }$ clockwise
4. $\theta =3^{\circ }$ anticlockwise

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.

When a plane mirror is rotated through an $\theta$ the reflected ray turns through angle $2\theta$ then the angle of deviation is :

1. $180-2(i-\theta )$
2. $90-2(i-\theta )$
3. $180-2(i+\theta )$
4. $90+2(i-\theta )$

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. A light of intensity $8{\text{kWm}}^{-2}$ falls on a plane mirror with reflection coefficient $r=0.95$. The angle of incidence is ${60}^{\circ }.$ The pressure exerted by the light on the mirror is

1. $1.3\times {10}^{-5}{\text{Nm}}^{-2}$
2. $0.3\times {10}^{-5}{\text{Nm}}^{-2}$
3. $30\times {10}^{-5}{\text{Nm}}^{-2}$
4. $1.3\times {10}^{-6}{\text{Nm}}^{-2}$

Q. A ray of light is incident on a glass plate making an angle of ${60}^{\circ }$ with the normal to the surface at the point of projection. If the reflected ray and refracted rays are perpendicular to each other, the refractive index of glass is :

1. $\sqrt{3}$
2. $\sqrt{\frac{3}{2}}$
3. $\frac{3}{2}$
4. $\frac{1}{2}$

Q. Light incident normally on a plane mirror attached to a galvanometercoil retraces backwards as shown in Fig. 9.36. A current in the coil produces a deflection of 3.5o of the mirror. What is the displacementof the reflected spot of light on a screen placed 1.5 m away?

Q. A ray of light making an angle ${10}^{\circ }$ with the horizontal is incident on a plane mirror making a angle $\theta$ with the horizontal. What should be the value of $\theta$ so that the reflected ray goes vertically upwards?

1. ${20}^{\circ }$
2. ${40}^{\circ }$
3. ${30}^{\circ }$
4. ${45}^{\circ }$

Q. An extended horizontal object $AB$ is placed in front of a plane mirror inclined at ${45}^{\circ }$ with horizontal as shown in the figure. The image of $AB$ in plane mirror will look like:

1. 
2. 
3. 
4. 

Q. An object is placed symmetrically between two plane mirrors inclined at an angle of ${72}^{\circ }$, then the total number of images observed will be

1. $5$
2. $4$
3. $3$
4. $2$

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 ray of light falls on a horizontal plane mirror at 60 degree .Through what angle, should the mirror be tilted to make the reflected ray horizontal?

Q. For a given incident ray, if the plane mirror is rotated through an angle of $\theta$ the reflected ray rotates through an angle

1. $\theta$
2. $2\theta$
3. $4\theta$
4. $\theta /2$