Question

a point object is kept in front of a plane mirror .the plane mirror is performing SHM of amplitude 2 cm .the plane mirror moves along the x-axis and x-axis is normal to the mirror .the amplitude of the mirror is such that object is always infront of the mirror .the amplitude of SHM of the image is

Answer 1

All measurements are in centimetres.
Let the point object be at a distance (x ,0) such that x is greater than 2.

When the mirror is at position x=-2, object distance = x - (-2) = x+2.
Image distance = x+2.

When the mirror is at position x=2, object distance = x-2
Image distance = x-2

Difference between image distances = |x-2 - (x+2)| = 4
Amplitude shall be half of this distance = 4/2 =2.

Hence, amplitude of the image shall also be 2cm.

Answer 2

vi =2 vm-vo

vi=2×2-0=4