(D) The magnification $m$ of a mirror is given by $m = \frac{f}{f - u}$.The image velocity $v_i$ is related to the object velocity $v_o$ by $v_i = -m^

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(D) The magnification $m$ of a mirror is given by $m = \frac{f}{f - u}$.The image velocity $v_i$ is related to the object velocity $v_o$ by $v_i = -m^2 v_o$.Given: Focal length $f = +20 \, cm = +0.2 \, m$ (convex mirror).Object distance $u = -2.8 \, m$.Object velocity $v_o = 15 \, m/s$.First,calculate the magnification $m$:$m = \frac{0.2}{0.2 - (-2.8)} = \frac{0.2}{3.0} = \frac{1}{15}$.Now,calculate the image velocity $v_i$:$v_i = -m^2 v_o = -(\frac{1}{15})^2 \times 15 = -\frac{1}{225} \times 15 = -\frac{1}{15} \, m/s$.The magnitude of the speed is $1/15 \, m/s$.

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

Difficult

$A$ convex mirror of focal length $20 \, cm$ is fitted in a car. $A$ second car,which is $2.8 \, m$ away,overtakes the first car at a relative speed of $15 \, m/s$. What will be the speed of the second car as observed in the mirror of the first car?

A
$0.1 \, m/s$
B
$0.15 \, m/s$
C
$1/10 \, m/s$
D
$1/15 \, m/s$

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Class 12 Questions

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Ray Optics and Optical Instruments

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Velocity in Mirrors (Kinematics)

$A$ 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

MediumAIEEE 2011

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An object is moving in front of a mirror as shown in the figure. Match the items in Column-$I$ with the values in Column-$II$.

$(i)$ Velocity of image $(a) \; 2 \; m/s$

$(ii)$ Velocity of image with respect to mirror $(b) \; 20 \; m/s$

$(iii)$ Velocity of image with respect to object $(c) \; 11 \; m/s$

$(iv)$ Velocity of image if mirror is stopped $(d) \; 22 \; m/s$

Medium

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If an object and a plane mirror both move towards each other with a velocity of $v$,what is the velocity of the image?

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Choose the correct statement$(s)$ related to the motion of an object and its image in the case of mirrors.

Medium

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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 $9\;cm/sec$. What is the velocity of the image at that instant?

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$(i)$ Velocity of image	$(a) \; 2 \; m/s$
$(ii)$ Velocity of image with respect to mirror	$(b) \; 20 \; m/s$
$(iii)$ Velocity of image with respect to object	$(c) \; 11 \; m/s$
$(iv)$ Velocity of image if mirror is stopped	$(d) \; 22 \; m/s$

$A$ convex mirror of focal length $20 \, cm$ is fitted in a car. $A$ second car,which is $2.8 \, m$ away,overtakes the first car at a relative speed of $15 \, m/s$. What will be the speed of the second car as observed in the mirror of the first car?

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$A$ 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

If an object and a plane mirror both move towards each other with a velocity of $v$,what is the velocity of the image?

Choose the correct statement$(s)$ related to the motion of an object and its image in the case of mirrors.

$A$ 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 $9\;cm/sec$. What is the velocity of the image at that instant?

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