(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)

The speed at which the image of a luminous point object is moving,if the luminous point object is moving at speed $v_0$ towards a spherical mirror along its axis,is (Given: $r =$ radius of curvature,$u =$ object distance):

Medium

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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:

MediumJEE MAIN 2020

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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:

Difficult

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The origin of $x$ and $y$ coordinates is the pole of a concave mirror of focal length $20\, cm$. The $x$-axis is the optical axis with $x > 0$ being the real side of the mirror. $A$ point object at the point $(25\, cm, 1\, cm)$ is moving with a velocity $10\, cm/s$ in the positive $x$-direction. The velocity of the image in $cm/s$ is approximately:

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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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The speed at which the image of a luminous point object is moving,if the luminous point object is moving at speed $v_0$ towards a spherical mirror along its axis,is (Given: $r =$ radius of curvature,$u =$ object distance):

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:

$A$ 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:

$A$ 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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