Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A point object is moving with a speed v before an arrangement of two mirrors as shown in fig. Find the velocity of image in mirror M 1 with respect to image in mirror M 2 .

Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Analyze the configuration of mirrors.
There are two mirrors, M1 and M2, inclined at an angle θ (let's assume it's 90° for simplicity in this explanation).
Step 2: Velocity of Image in Mirror M1
The image formed in M1 (let's call it I1) will move in the opposite direction to the object. Thus:
Velocity of image I1, \( v_{I1} = -v
Step 3: Velocity of Image in Mirror M2
The image formed in M2 (let's call it I2) will also move but it will be determined by the velocity of I1 since it is the image of the object reflected by M1.
If M1 reflects I1, then I2 moves in the direction against the incoming image character, giving us:
Velocity of image I2, \( v_{I2} = -v_{I1} = v
Step 4: Relative Velocity
Now to find the velocity of image I1 with respect to image I2, we compute:
\( v_{relative} = v_{I1} - v_{I2} = -v - v = -2v
Conclusion:
The velocity of the image in mirror M1 with respect to the image in mirror M2 is \( -2v \).
Therefore, the answer is A.
There are two mirrors, M1 and M2, inclined at an angle θ (let's assume it's 90° for simplicity in this explanation).
Step 2: Velocity of Image in Mirror M1
The image formed in M1 (let's call it I1) will move in the opposite direction to the object. Thus:
Velocity of image I1, \( v_{I1} = -v
Step 3: Velocity of Image in Mirror M2
The image formed in M2 (let's call it I2) will also move but it will be determined by the velocity of I1 since it is the image of the object reflected by M1.
If M1 reflects I1, then I2 moves in the direction against the incoming image character, giving us:
Velocity of image I2, \( v_{I2} = -v_{I1} = v
Step 4: Relative Velocity
Now to find the velocity of image I1 with respect to image I2, we compute:
\( v_{relative} = v_{I1} - v_{I2} = -v - v = -2v
Conclusion:
The velocity of the image in mirror M1 with respect to the image in mirror M2 is \( -2v \).
Therefore, the answer is A.
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