Reflection & Mirrors

If a parallel beam of light is incident on spherical mirrors then after reflection they pass through focal point. If F is the focal length and R is the radius of curvature of mirror then

In parallax method for the determination of focal length of a concave mirror, the object should always be placed:

A concave mirror of focal length 10 cm forms an image which is double the size of object when the object is placed at two different positions. The distance between the two positions of the object is ______ cm.

Distance between an object and three times magnified real image is 40 cm. The focal length of the mirror used is ______ cm.

A rod of length 10 cm lies along the principle axis of a concave mirror of focal length 10 cm as shown in figure. The length of the image is ______ cm.

A concave mirror of focal length $f$ in air is dipped in a liquid of refractive index $\mu$. Its focal length in the liquid will be:

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm, at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is:

Distance between object and its image (magnified by $-\frac{1}{3}$) is 30 cm. The focal length of the mirror used is $\left(\frac{x}{4}\right)\text{cm}$, where magnitude of value of $x$ is _________.

The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature $\text{R} = 2\text{ m}$. Another car approaches him from behind with a uniform speed of $90\text{ km/hr}$. When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is ' $a$ '. The value of $100a$ is __________ $\text{m/s}^2$.

A mirror is used to produce an image with magnification of $\frac{1}{4}$. If the distance between object and its image is 40 cm, then the focal length of the mirror is ________.

When an object is placed 40 cm away from a spherical mirror an image of magnification $\frac{1}{2}$ is produced. To obtain an image with magnification of $\frac{1}{3}$, the object is to be moved:

A concave mirror produces an image of an object such that the distance between the object and image is 20 cm. If the magnification of the image is –3, then the magnitude of the radius of curvature of the mirror is:

The image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $\frac{25}{3}\text{ m}$ to $\frac{50}{7}\text{ m}$ in 30 second. The speed of the object in $\text{km/hr}$ is

A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is:

A plane mirror produces a magnification of

Given below are two statements:

Statement I: Image formation needs regular reflection and/or refraction.

Statement II: The variety in colour of objects we see around us is due to the constituent colours of the light incident on them.

In the light of the above statements, choose the most appropriate answer from the options given below:

A convex mirror of radius of curvature $30\text{ cm}$ forms an image that is half the size of the object. The object distance is:

A concave mirror of focal length ' $f$ ' produces an image ' $n$ ' time the size of the object. If the image is real, then the distance of the object from the mirror is

If the distance between object and its two times magnified virtual image produced by a curved mirror is $15\text{ cm}$, the focal length of the mirror must be:

When one light ray is reflected from a plane mirror with $30^\circ$ angle of reflection, the angle of deviation of the ray after reflection is:

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer is :-

A. Real

B. Erect

C. Smaller in size than object

D. Laterally inverted

Choose the most appropriate answer from the options given below:

To get three images of a single object, the angle between the two plane mirrors should be

An object is placed at a distance of 12 cm in front of a plane mirror. The virtual and erect image is formed by the mirror. Now the mirror is moved by 4 cm towards the stationary object. The distance by which the position of image would be shifted, will be

Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is _______________.

Two vertical parallel mirrors A and B are separated by $10\text{ cm}$. A point object $\text{O}$ is placed at a distance of $2\text{ cm}$ from mirror $\text{A}$. The distance of the second nearest image behind mirror A from the mirror $\text{A}$ is _________ $\text{cm}$.

A thin cylindrical rod of length $10\text{ cm}$ is placed horizontally on the principal axis of a concave mirror of focal length $20\text{ cm}$. The rod is placed in such a way that mid point of the rod is at $40\text{ cm}$ from the pole of mirror. The length of the image formed by the mirror will be $\frac{x}{3}\text{ cm}$. The value of $x$ is _____________.

In an experiment for estimating the value of focal length of converging mirror, image of an object placed at $40\text{ cm}$ from the pole of the mirror is formed at distance $120\text{ cm}$ from the pole of the mirror. These distances are measured with a modified scale in which there are 20 small divisions in $1\text{ cm}$. The value of error in measurement of focal length of the mirror is $\frac{1}{\text{K}}\text{ cm}$. The value of $\text{K}$ is __________.

A light ray is incident, at an incident angle $\theta$1, on the system of two plane mirrors M1 and M2 having an inclination angle 75$^\circ$ between them (as shown in figure). After reflecting from mirror M1 it gets reflected back by the mirror M2 with an angle of reflection 30$^\circ$. The total deviation of the ray will be _____________ degree.

An object 'O' is placed at a distance of $100\text{ cm}$ in front of a concave mirror of radius of curvature $200\text{ cm}$ as shown in the figure. The object starts moving towards the mirror at a speed $2\text{ cm/s}$. The position of the image from the mirror after $10\text{ s}$ will be at _________ $\text{cm}$.

The focal length f is related to the radius of curvature r of the spherical convex mirror by:

An object is placed beyond the centre of curvature C of the given concave mirror. If the distance of the object is d1 from C and the distance of the image formed is d2 from C, the radius of curvature of this mirror is:

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors$\vec{a},\ \vec{b}$, and $\vec{c}$respectively. Then choose the correct relation for these vectors.

Two plane mirrors M1 and M2 are at right angle to each other shown. A point source 'P' is placed at 'a' and '2a' meter away from M1 and M2 respectively. The shortest distance between the images thus formed is: (Take $\sqrt{5}$ = 2.3)

Car B overtakes another car A at a relative speed of 40 ms${}^{-1}$. How fast will the image of car B appear to move in the mirror of focal length 10 cm fitted in car A, when the car B is 1.9 m away from the car A?

A short straight object of height 100 cm lies before the central axis of a spherical mirror whose focal length has absolute value | f | = 40 cm. The image of object produced by the mirror is of height 25 cm and has the same orientation of the object. One may conclude from the information:

A point source of light S, placed at a distance 60cm in front of the centre of a plane mirror of width 50 cm, hangs vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 1.2 m from it (see in the figure). The distance between the extreme points where he can see the image of the light source in the mirror is __________ cm.

An object is placed on the principal axis of a concave mirror at a distance of $1.5f$ ($f$ is the focal length). The image will be at,

A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object?

(Figure drawn as schematic and not to scale)

An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror. The graphical representation of the magnitude of linear magnification (m) versus distance of the object from the mirror (x) is correctly given by:

(Graphs are drawn schematically and are not to scale)

When an object is kept at a distance of 30 cm from a concave mirror, the image is formed at a distance of 10 cm from the mirror. If the object is moved with a speed of 9 cms–1, the speed (in cms–1) with which image moves at that instant is ____.

A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:

Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror (M1) and parallel to the second mirror (M2) is finally reflected from the second mirror (M2) parallel to the first mirror (M1). The angle between the two mirrors will be:

A point source of light, S is placed at distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance 2L as shown below. The distance over which the man can see the image of the light source in the mirror is

An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be

A particle is oscillating on the $X$-axis with an amplitude $2\text{ cm}$ about the point $x_0 = 10\text{ cm},$ with a frequency $\omega$. A concave mirror of focal length $5\text{ cm}$ is placed at the origin (see figure).

Identify the correct statements.

(A) The image executes periodic motion.

(B) The image executes non-periodic motion.

(C) The turning points of the image are asymmetric w.r.t. the image of the point at $x = 10\text{ cm}$. (D) The distance between the turning points of the oscillation of the image is $\frac{100}{21}\text{ cm.}$

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

Match the corresponding entries of column 1 with column 2. [Where m is the magnification

produced by the mirror]

You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be:

Two plane mirrors are inclined at 70°. A ray incident on one mirror at angle, $\theta$ after reflection falls on second mirror and is reflected from there parallel to first mirror. The value of $\theta$ is

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its end closer to the pole is 20 cm away from the mirror. The length of the image is

A car is fitted with a convex side-view mirror of focal length $20\text{ cm}$. A second car $2.8\text{ m}$ behind the first car is overtaking the first car at a relative speed of $15\text{ m/s}$. The speed of the image of the second car as seen in the mirror of the first one is:

To get three images of a single object, one should have two plane mirrors at an angle of

If two mirrors are kept at $60^\circ$ to each other, then the number of images formed by them is

A tall man of height 6 feet, want to see his full image. Then required minimum length of the mirror will be