(C) Let the position of the object be $x_O$ and the position of the mirror be $x_M$. The position of the image $x_I$ is given by the relation $x_I - x

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(C) Let the position of the object be $x_O$ and the position of the mirror be $x_M$. The position of the image $x_I$ is given by the relation $x_I - x_M = -(x_O - x_M)$,which simplifies to $x_I = 2x_M - x_O$.Since the object is stationary,$x_O$ is constant,so $v_O = 0$.Differentiating with respect to time,we get the velocity of the image: $v_I = 2v_M - v_O = 2v_M$.Integrating or considering the displacement,the amplitude of the image $A_I$ is related to the amplitude of the mirror $A_M$ by $A_I = 2A_M$.Given $A_M = 2 \ cm$,the amplitude of the image is $A_I = 2 \times 2 \ cm = 4 \ cm$.

Class 12 Physics Ray Optics and Optical Instruments Velocity in Mirrors (Kinematics)

Medium

$A$ point object is kept in front of a plane mirror. The plane mirror is performing $SHM$ with an amplitude of $2 \ cm$. The plane mirror moves along the $x-$ axis,which is normal to the mirror. The amplitude of the mirror is such that the object is always in front of the mirror. The amplitude of the $SHM$ of the image is .... $cm$.

A
$0$
B
$2$
C
$4$
D
$1$

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Ray Optics and Optical Instruments

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Velocity in Mirrors (Kinematics)

$A$ plane mirror is moving with velocity $4\hat i + 5\hat j + 8\hat k$. $A$ point object in front of the mirror moves with a velocity $3\hat i + 4\hat j + 5\hat k$. Here,the $\hat k$ direction is along the normal to the plane mirror and facing towards the object. The velocity of the image is:

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$A$ luminous point object is moving along the principal axis of a concave mirror of focal length $12 \ cm$ towards it. When its distance from the mirror is $20 \ cm$,its velocity is $4 \ cm/s$. The velocity of the image in $cm/s$ at that instant is:

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An object approaches a convex mirror of radius of curvature $20 \,m$ along its optical axis. The image is observed to move from $\frac{25}{3} \,m$ to $\frac{50}{7} \,m$ from the mirror in $30 \,s$. What is the speed of the object in $km/h$?

IIT 2010

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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 $A$? (In $ms^{-1}$)

DifficultJEE MAIN 2021

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

DifficultMHT CET 2025

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$A$ plane mirror is moving with velocity $4\hat i + 5\hat j + 8\hat k$. $A$ point object in front of the mirror moves with a velocity $3\hat i + 4\hat j + 5\hat k$. Here,the $\hat k$ direction is along the normal to the plane mirror and facing towards the object. The velocity of the image is:

$A$ luminous point object is moving along the principal axis of a concave mirror of focal length $12 \ cm$ towards it. When its distance from the mirror is $20 \ cm$,its velocity is $4 \ cm/s$. The velocity of the image in $cm/s$ at that instant is:

An object approaches a convex mirror of radius of curvature $20 \,m$ along its optical axis. The image is observed to move from $\frac{25}{3} \,m$ to $\frac{50}{7} \,m$ from the mirror in $30 \,s$. What is the speed of the object in $km/h$?

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 $A$? (In $ms^{-1}$)

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

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