An observer is standing at a point O, at a distance of 100 cm from a convex lens of focal length 50 cm. A plane mirror is placed behind the lens at a distance of 150 cm from the lens. The magnitude and direction of velocity of her own image as seen by the observer, at the moment when the mirror just starts moving (left or right) with a velocity of 10 cm/s.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

Is $\frac{10}{9} cm / s$ towards right

Is $\frac{10}{9} cm / s$ towards left

Is $\frac{20}{9} cm / s$ towards right

Is $\frac{20}{9} cm / s$ towards left

answer is B, D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

${\vec{V}}_{I} = 2 {\vec{V}}_{m} - {\vec{V}}_{0} \Rightarrow {\vec{V}}_{I} = 2 {\vec{V}}_{m}$
Velocity of image in the plane mirror will be 20 cm/s in the direction of motion of mirror.

Now for 2nd refraction is lens:
$\begin{array}{l} V = \frac{200}{3} \\ ∵ |\frac{dv}{dt}| = \frac{v^{2}}{u^{2}} |\frac{du}{dt}| = \frac{20}{9} cm / s \end{array}$