A real 1 mm long object is kept perpendicular to the principal axis of a concave mirror. The size of the image formed is 1/4 mm. Now the mirror starts moving, away, from the object with a velocity 2 cm/s along the principal axis.

Options

A. the velocity of the image along the principal axis at the given instant will be `(17)/(8) cm//s` towards the mirror
B. the length of the image will decrease as the mirror moves
C. the speed of the image will always be more than `2 cm//s`
D. the rate with which the length of the image will change is a constant

Answer

A, B, C

Explanation

Lateral magnification `= (1)/(4)`
With respect to mirror :
velocity of object = 2 cm/s towards left
velocity of image `=((1)/(4))^(2) xx 2 cm//s` towards right `=(2)/(16)=(1)/(8)`
With respect to the ground velocity of image `=((1)/(8)+2)(cm)/(s)` towards right `(17)/(8)(cm)/(s)` towards right.