Image of Point Object in Plane Mirror

Q. Two plane mirrors A and B are aligned parallel to each as shown in the figure. A light ray is incident at an angle of ${30}^{\circ }$ at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is

1. $28$
2. $34$
3. $30$
4. $32$

Q.

The image formed by plane mirror is ________.

Q. Three plane mirrors are arranged mutually perpendicular to each other as shown in the figure. If a point object is placed symmetrically between the mirrors, then the number of distinct images formed will be

1. $6$
2. $7$
3. $8$
4. $9$

Q. When a beam of light is incident on a plane mirror, it is found that a real image is formed. The incident light beam must be

1. Converging
2. Diverging
3. Parallel
4. Formation of real image by plane mirror is not possible.

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. A fluorescent lamp of length 1m is placed horizontal at a depth of 1.2 m below a ceiling.a plane mirror of length 0.6 m is placed below the lamp parallel to and symmetric to the lamp at a distance of 2.4 m from it.the length of reflected path of the light on the celling is

Q.

Sun rays are reflected from a horizontal mirror and falls on a vertical screen .a vertical object of height h is placed on the mirror .length of the shadow on the screen is?

Q. An object is moving vertically upward at speed of V as shown in figure. Velocity of image from mirror inclined at angle of ${37}^{\circ }$ from horizontal is

1. ($\frac{24}{25}\hat{i}+\frac{7}{25}\hat{j}$)V
2. ($\frac{7}{25}\hat{i}-\frac{24}{25}\hat{j}$)V
3. ($\frac{7}{25}\hat{i}+\frac{24}{25}\hat{j}$)V
4. ($\frac{24}{25}\hat{i}-\frac{7}{25}\hat{j}$)V

Q. An unpolarized light beam is incident on a surface at an angle of incidence equal to Brewster's angle. Then,

1. the reflected and the refracted beams are both partially polarized.
2. the reflected beam is partially polarized and the refracted beam is completely polarized and are at right angles to each other.
3. the reflected beam is completely polarized and the refracted beam is partially polarized and are at right angles to each other.
4. both the reflected and the refracted beams are completely polarized and are at right angles to each other.

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

Q. Two mirrors are inclined at an angle ${60}^{\circ }$. If an object is placed symmetrically between them, then the number of images formed will be

1. $3$
2. $4$
3. $5$
4. $6$

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. ${30}^{\circ }$ from $M_1$ and ${20}^{\circ }$ from $M_2$
2. ${50}^{\circ }$ from $M_1$ and ${40}^{\circ }$ 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. For the given incident ray as shown in the figure, the condition for total internal reflection will be satisfied if the refractive index of the block is greater than

1. $\frac{\sqrt{3}+1}{2}$
2. $\sqrt{\frac{5}{2}}$
3. $\sqrt{\frac{3}{2}}$
4. $\sqrt{\frac{7}{2}}$

Q. Two plane mirrors are placed perpendicular to each other and a point object $P$ is placed equidistant from both the mirrors. Find the equation of the geometerical shape at which the images of the object will lie.

1. $x^2+y^2=2$
2. $x^2+y^2=8$
3. $x+y=2$
4. $y=x$

Q. A plane mirror is inclined at an angle $\theta ={37}^{\circ }$ with horizontal surface. A particle is projected from point $P$ (see figure) at $t=0$ with a velocity $v=20\text{m/s}$ at an angle $\alpha ={53}^{\circ }$ with horizontal. Assuming the particle does not collide with the mirror. If in time $t$ (in $\text{s}$), image will be momentarily at rest with respect to particle, Find $10t$.

Q. In the proof that a person requires a plane mirror at least half of his is height, it is shown that the the reflected rays actually intersect each other but how this is possible because a plane mirror always produces a virtual and erect image.

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

Q. For the arrangement of plane mirrors as shown in the figure where the length of the mirrors $M_1$ and $M_2$ are equal, find the number of images formed if a point object $O$ is placed at the centroidal position.

1. $21$
2. $14$
3. $17$
4. $24$

Q. Four identical mirrors are used to form a square arrangement as shown in top view of the figure. A ray starts from mid-point m of mirror AD and after two reflections, reaches corner D, then angle$\theta =co{t}^{-1}n$.Here n is

Q.

Look at Fig. Can the image of the child in it be obtained on a screen?

Q.

A point source of light B is placed at a distance L in front of the centre of a mirror of width d hung vertically on a wall. A man walks in front of themirror along a line parallel to the mirror at a distance 2L from it as shown. The greatest distance over which he can see the image of the light source in the mirror is

[IIT-JEE (Screening) 2000]

1. 2d

2. 3d

3. d

4. d/2

Q. A moth is at a distance of $10cm$ in front of a plane mirror. An observer is standing at a distance of $30cm$ in front of the mirror. Calculate the distance between the observer and the position of the moth's image.

1. $30cm$
2. $50cm$
3. $10cm$
4. $40cm$

Q.

Can real image be obtained on the screen?

Q. A small object is placed $10cm$ in front of a plane mirror. If you stand behind the object $30cm$ from the mirror and look at its image, the distance focused for your eye will be:

1. $60$cm
2. $20$cm
3. $40$cm
4. $80$cm

Q. Column I represents the angle at which two mirrors are inclined and column II represents number of images formed in the arrangement. Select the option that correctly matches the number of images formed with the arrangement for an object placed asymmetrical from the mirrors.

Column I	Column II
$\left(a\right)\theta ={60}^{\circ }$	$\left(1\right)n=1$
$\left(b\right)\theta ={40}^{\circ }$	$\left(2\right)n=3$
$\left(c\right)\theta ={90}^{\circ }$	$\left(3\right)n=5$
$\left(d\right)\theta ={180}^{\circ }$	$\left(4\right)n=9$

1. $\left(a\right)\to \left(3\right),\left(b\right)\to \left(4\right),\left(c\right)\to \left(2\right),\left(d\right)\to \left(1\right)$
2. $\left(a\right)\to \left(2\right),\left(b\right)\to \left(3\right),\left(c\right)\to \left(1\right),\left(d\right)\to \left(4\right)$
3. $\left(a\right)\to \left(3\right),\left(b\right)\to \left(4\right),\left(c\right)\to \left(1\right),\left(d\right)\to \left(2\right)$
4. $\left(a\right)\to \left(2\right),\left(b\right)\to \left(3\right),\left(c\right)\to \left(4\right),\left(d\right)\to \left(1\right)$

Q. Use the mirror equation to deduce that:
(a) an object placed between $f$ and $2f$ of a concave mirror produces a real image beyond $2f$.
(b) a convex mirror always produces a virtual image independent of the location of the object.
(c) the virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole.
(d) an object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.
[Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]

Q. When a plane mirror is rotated through an angle $\theta ,$ the reflected ray turms an angle $2\theta$ , then the size of the image is

1. Halved
2. Doubled
3. Remains the same
4. Becomes infinite

Q. Two plane mirrors, $\text{A}$ and $\text{B}$ are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle of ${30}^{\circ }$ at a point just inside one end of $\text{A}.$ The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is-

1. $28$
2. $30$
3. $32$
4. $34$

Q.

State three characteristics of an image formed by a mirror?

Q. 45. A person 1.6m tall is standing at the centre between two walls 3 m high. what is the minimum size of a plane mirror fixed on the wall in front of him , if he is to see the full height of the wall behind him?