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 hemispherical portion of the surface of a solid glass sphere (μ = 1.5) of radius r is silvered to make the inner side reflecting. An object is placed on the axis of the hemisphere at a distance 3r from the centre of the sphere. The light from the object is refracted at the unsilvered part, then reflected from the silvered part and again refracted at the unsilvered part. Locate the final image formed.

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

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. circle
4. ellipse

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. 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. circle
4. ellipse

Q. A solid glass sphere with radius $1\text{m}$ and an index of refraction $1.5$ is silvered over one hemisphere. A small object is located on the axis of the sphere at a distance $2\text{m}$ to the left of the vertex of the unsilvered hemisphere. The position of final image after all refractions and reflections have taken place is

1. at vertex of silvered face
2. at object itself
3. at centre of curvature
4. at vertex of unsilvered face

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