(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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Class 12 Questions

Class 12

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Ray Optics and Optical Instruments

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Velocity in Mirrors (Kinematics)

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 $9\, cm/s$,the speed (in $cm/s$) with which the image moves at that instant is:

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The bob of a pendulum is released from position $P$. What is the velocity of the image of the bob on the mirror $M$ at position $Q$ with respect to the bob?

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$A$ point object is moving on the principal axis of a concave mirror of focal length $24 \; cm$ towards the mirror. When it is at a distance of $60 \; cm$ from the mirror,its velocity is $9 \; cm/s$. What is the velocity of the image at that instant?

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$A$ plane mirror is placed along the $x$-axis facing the negative $y$-axis. The mirror is fixed. $A$ point object is moving with a velocity of $3\hat{i} + 4\hat{j}$ in front of the plane mirror. Find the relative velocity of the image with respect to the object.

Medium

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$A$ particle is moving with velocity $\vec{v}_p = (\hat{i} + 2\hat{j} + 3\hat{k}) \text{ m/s}$. $A$ plane mirror exists in the $x-y$ plane. The mirror has a velocity $\vec{v}_m = (\hat{i} + 2\hat{j}) \text{ m/s}$. The velocity of the image (in $\text{m/s}$) is:

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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 $9\, cm/s$,the speed (in $cm/s$) with which the image moves at that instant is:

The bob of a pendulum is released from position $P$. What is the velocity of the image of the bob on the mirror $M$ at position $Q$ with respect to the bob?

$A$ point object is moving on the principal axis of a concave mirror of focal length $24 \; cm$ towards the mirror. When it is at a distance of $60 \; cm$ from the mirror,its velocity is $9 \; cm/s$. What is the velocity of the image at that instant?

$A$ plane mirror is placed along the $x$-axis facing the negative $y$-axis. The mirror is fixed. $A$ point object is moving with a velocity of $3\hat{i} + 4\hat{j}$ in front of the plane mirror. Find the relative velocity of the image with respect to the object.

$A$ particle is moving with velocity $\vec{v}_p = (\hat{i} + 2\hat{j} + 3\hat{k}) \text{ m/s}$. $A$ plane mirror exists in the $x-y$ plane. The mirror has a velocity $\vec{v}_m = (\hat{i} + 2\hat{j}) \text{ m/s}$. The velocity of the image (in $\text{m/s}$) is:

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