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Question
A point object is kept in front of a plane mirror. The plane mirror is doing SHM of amplitude 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 SHM of the image is
A point object is kept in front of a plane mirror. The plane mirror is doing SHM of amplitude 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 SHM of the image is
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Solution
The correct option is C 4cm
Assume the mirror is at the origin and it is moving about the origin along x direction between x = -2 and x = +2 as its extreme positions.
Assume that the object is placed at co=ordinate of x = - (2+x)
So, when mirror is at position x = -2, the object's image will be formed at x co-ordinate X = - 2+x
And when the mirror is at position x = +2, the image is formed at X = 6+x
So, the net difference in the position of image between these 2 co-ordinates is ( 6 + x ) - ( -2 + x ) = 8
So, the amplitude will be half of this distance. So the answer is 8/2 = 4 cm.
Option C is correct.
Assume the mirror is at the origin and it is moving about the origin along x direction between x = -2 and x = +2 as its extreme positions.
Assume that the object is placed at co=ordinate of x = - (2+x)
So, when mirror is at position x = -2, the object's image will be formed at x co-ordinate X = - 2+x
And when the mirror is at position x = +2, the image is formed at X = 6+x
So, the net difference in the position of image between these 2 co-ordinates is ( 6 + x ) - ( -2 + x ) = 8
So, the amplitude will be half of this distance. So the answer is 8/2 = 4 cm.
Option C is correct.
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