Spherical Mirror

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A short linear object of length $b$ lies along the axis of a concave mirror of focal length $f$ at a distance $u$ from the pole of the mirror. The size of the image is approximately equal to

b (\frac{u - f}{f})^{1/2}

(B)

b (\frac{f}{u - f})^{1/2}

(C)

b (\frac{u - f}{f})

(D)

b (\frac{f}{u - f})^{2}

LEVELJEE Advanced

A concave mirror is placed on a horizontal table with its axis directed vertically upwards. Let $O$ be the pole of the mirror and $C$ its centre of curvature. A point object is placed at $C$ . It has a real image, also located at $C$ . If the mirror is now filled with water, the image will be

(A)

real and will remain at

C

(B)

real and located at a point between

C

and

\infty

(C)

virtual and located at a point between

C

and

O

(D)

real and located at a point between

C

and

O

JEE Advanced 1991

LEVELJEE Advanced

A thin rod of length $\frac{f}{3}$ is placed along the optic axis of a concave mirror of focal length $f$ such that its image which is real and elongated, just touches the rod. The magnification is ......

JEE Advanced 2010

LEVELJEE Main

Image of an object approaching a convex mirror of radius of curvature $20 m$ along its optical axis is observed to move from $\frac{25}{3} m$ to $\frac{50}{7} m$ in $30 s$ . What is the speed of the object in $km h^{- 1}$ ?

JEE Advanced 2008

LEVELJEE Main

An optical component and an object $S$ placed along its optic axis are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I.

List-I

List-II

A container is filled with water ( $μ = 1.33$ ) up to a height of $33.25 cm$ . A concave mirror is placed $15 cm$ above the water level and the image of an object placed at the bottom is formed $25 cm$ below the water level. The focal length of the mirror is

(A)

10 cm

(B)

15 cm

(C)

20 cm

(D)

25 cm

LEVELJEE Advanced

A student performed the experiment of determination of focal length of a concave mirror by $u$ - $v$ method using an optical bench of length $1.5 m$ . The focal length of the mirror used is $24 cm$ . The maximum error in the location of the image can be $0.2 cm$ . The 5 sets of $(u, v)$ values recorded by the student (in cm) are : (42, 56), (48, 48), (60, 40), (66, 33), (78, 39). The data set(s) that cannot come from experiment and is (are) incorrectly recorded, is (are)

* Multiple Correct Options

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $f$ as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)

In an experiment to determine the focal length ( $f$ ) of a concave mirror by the $u$ - $v$ method, a student places the object pin $A$ on the principal axis at a distance $x$ from the pole $P$ . The student looks at the pin and its inverted image from a distance keeping his/her eye in line with $P A$ . When the student shifts his/her eye towards left, the image appears to the right of the object pin. Then

(A)

x < f

(B)

f < x < 2 f

(C)

x = 2 f

(D)

x > 2 f

LEVELJEE Main

Assertion The formula connecting $u$ , $v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature. Reason Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

(A)

If Assertion is true, Reason is true; Reason is the correct explanation for Assertion.

(B)

If Assertion is true, Reason is true; Reason is not a correct explanation for Assertion.

(C)

If Assertion is true; Reason is false.

(D)

If Assertion is false; Reason is true.

JEE Advanced 2025

LEVELJEE Advanced

Two identical concave mirrors each of focal length $f$ are facing each other as shown in the schematic diagram. The focal length $f$ is much larger than the size of the mirrors. A glass slab of thickness $t$ and refractive index $n_{0}$ is kept equidistant from the mirrors and perpendicular to their common principal axis. A monochromatic point light source $S$ is embedded at the center of the slab on the principal axis, as shown in the schematic diagram. For the image to be formed on $S$ itself, which of the following distances between the two mirrors is/are correct:

* Multiple Correct Options

(A)

4 f + (1 - \frac{1}{n _{0}}) t

(B)

2 f + (1 - \frac{1}{n _{0}}) t

(C)

4 f + (n_{0} - 1) t

(D)

2 f + (n_{0} - 1) t

JEE Advanced 2016

LEVELJEE Advanced

A small object is placed 50 cm to the left of thin convex lens of focal length 30 cm. A convex spherical mirror of radius of curvature 100 cm is placed to the right of the lens at a distance of 50 cm. The mirror is tilted such that the axis of the mirror is at an angle $θ = 3 0^{\circ}$ 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 (in cm) of the point (x, y) at which the image is formed are :

(A)

(25, 253)

(B)

(\frac{125}{3}, \frac{25}{3})

(C)

(50 - 253, 25)

(D)

(0, 0)

JEE Advanced 2018

LEVELJEE Advanced

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length f, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire ? (These figures are not to scale.) ?

An object and a concave mirror of focal length $f = 10 cm$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_{0} = 15 cm s^{- 1}$ towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by $u$ . When $u = 30 cm$ , the speed of the mirror $V_{m}$ is such that the image is instantaneously at rest with respect to the laboratory frame, and the object forms a real image. The magnitude of $V_{m}$ is ________ $cm s^{- 1}$ .

JEE Main 2019

LEVELJEE Main

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

(A)

0.16 m

(B)

1.60 m

(C)

0.32 m

(D)

0.24 m

JEE Main 2020

LEVELJEE Main

A spherical mirror is obtained as shown in the above figure from a hollow glass sphere. If an object is 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)

(A)

Erect, virtual and unmagnified

(B)

Inverted, real and magnified

(C)

Erect, virtual and magnified

(D)

Inverted, real and unmagnified

JEE Main 2021

LEVELJEE Main

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)

4 ms^{- 1}

(B)

0.2 ms^{- 1}

(C)

40 ms^{- 1}

(D)

0.1 ms^{- 1}

LEVELJEE Advanced

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

(A)

\frac{1}{15} m/s

(B)

10 m/s

(C)

15 m/s

(D)

\frac{1}{10} m/s

JEE Main 2021

LEVELBoard

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

(A)

f = r

(B)

f = - r

(C)

f = - \frac{r}{2}

(D)

f = + \frac{r}{2}

JEE Main 2020

LEVELJEE Main

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 ........... .

JEE Main 2021

LEVELJEE Main

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)

Image is real, same side of concave mirror

(B)

Image is virtual, opposite side of concave mirror

(C)

Image is real, same side of convex mirror

(D)

Image is virtual, opposite side of convex mirror

JEE Main 2021

LEVELJEE Advanced

An object is placed beyond the centre of curvature $C$ of the given concave mirror. If the distance of the object is $d_{1}$ from $C$ and the distance of the image formed is $d_{2}$ from $C$ , the radius of curvature of this mirror is

(A)

\frac{2 d _{1} d _{2}}{d _{1} - d _{2}}

(B)

\frac{2 d _{1} d _{2}}{d _{1} + d _{2}}

(C)

\frac{d _{1} d _{2}}{d _{1} + d _{2}}

(D)

\frac{d _{1} d _{2}}{d _{1} - d _{2}}

JEE Main 2020

LEVELJEE Main

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)

List-I

List-II

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length f, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire ? (These figures are not to scale.) ?

A spherical mirror is obtained as shown in the above figure from a hollow glass sphere. If an object is 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)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The focal length f is related to the radius of curvature r of the spherical convex mirror by

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