Image of Point Object in Plane Mirror

Q. Two mirrors are inclined at an angle of ${30}^{\circ }$. An object is placed making an angle of ${10}^{\circ }$ with mirror $M_1$. The position of the second image formed by mirrors $M_1$ and $M_2$ with respect to mirrors $M_1$ and $M_2$ respectively will be

1. ${50}^{\circ }$ from $M_1$ and ${40}^{\circ }$ from $M_2$
2. ${30}^{\circ }$ from $M_1$ and ${20}^{\circ }$ from $M_2$
3. ${70}^{\circ }$ from $M_1$ and ${40}^{\circ }$ from $M_2$
4. ${10}^{\circ }$ from $M_1$ and ${80}^{\circ }$ from $M_2$

Q. A plane mirror with reflecting surface facing along $+y$ - axis is placed along $+x$ - axis. The equation of a linear object kept in front of the mirror is $y=x$ as shown in figure. The equation of its image will be

1. $y-x=0$
2. $y+x=0$
3. $2y+x=0$
4. $y+2x=0$

Q. A plane mirror hinged at O is free to rotate in a vertical plane. The point O is at a distance x from a long screen placed in front of the mirror as shown in figure. A laser beam of light incident vertically downward is reflected by he mirror at O so that a bright spot is formed at the screen.
At the instant shown, the angle of inclidence is $\theta$ and the mirror is rotating clockwise with constant angular velocity w. Find the speed of the spot at this instant.

1. $2xwse{c}^2\varphi$
2. $2xwco{s}^2\varphi$
3. $2xwsi{n}^2\varphi$
4. $2xwta{n}^2\varphi$

Q.

It is desired to photograph the image of an object placed at a distance of 3 m from the plane mirror. The camera which is at a distance of 4.5 m from the mirror should be focussed for a distance of

1. 6m

2. 4.5m

3. 6m

4. 7.5m

Q. A plane mirror is inclined at an angle of ${45}^{\circ }$ with the horizontal and having one of its end at the origin(O) as shown in figure. An object is kept at $x=-2\text{cm}$. The position coordinates of the image of $P$ will be

1. $(+2,0)\text{cm}$
2. $(0,+2)\text{cm}$
3. $(0,0)\text{cm}$
4. $(0,-2)\text{cm}$

Q. We define an image formed by a plane mirror to be a 'Virtual' image when

1. the reflected rays coming to our eyes from the mirror don’t meet at the object
2. the reflected rays coming to our eyes from the mirror actually meet at a certain point
3. the reflected rays coming to our eyes from the mirror only appear to be meeting at a certain point
4. the reflected rays coming to our eyes from the mirror don't appear to be meeting at any point.

Q. Consider the situation of the previous problem. If the mirror reflects only 64% of the light energy falling on it, what will be the ratio of the maximum to the minimum intensity in the interference pattern observed on the screen?

Q. A plane mirror hinged at O is free to rotate in a vertical plane. The point O is at a distance x from a long screen placed in front of the mirror as shown in figure. A laser beam of light incident vertically downward is reflected by he mirror at O so that a bright spot is formed at the screen.
At the instant shown, the angle of inclidence is $\theta$ and the mirror is rotating clockwise with constant angular velocity w. Find the speed of the spot at this instant.

1. $2xwse{c}^2\varphi$
2. $2xwco{s}^2\varphi$
3. $2xwsi{n}^2\varphi$
4. $2xwta{n}^2\varphi$