Optics Question 785
Question: A point object is located at a distance 15cm. from the pole of a concave mirror of focal length 10cm on its principal axis is moving with a velocity $ (8\hat{i}+11\hat{j}) $ cm/s and velocity of mirror is $ (4\hat{i}+2\hat{j}) $ cm/s as shown. If $ \vec{v} $ is the velocity of image. Then find the value of $ | {\vec{v}} | $ in (cm/s).
Options:
A) 20
B) 30
C) 10
D) 40
Show Answer
Answer:
Correct Answer: A
Solution:
[a] $ {{\vec{v}} _{obj,moier}}=4\hat{i}+9\hat{j} $
$ \frac{dx}{dt}=4,\frac{dy}{dt}=9,u=-x $
$ -\frac{1}{10}=\frac{1}{V}+\frac{1}{-x};V=\frac{-10x}{x-10} $
$ v _{ix}=\frac{dV}{dt}={{( \frac{10}{x-10} )}^{2}}( \frac{dx}{dt} );v _{ix}=-16 $
$ m=-\frac{V}{-x}=\frac{-10}{x-10}=\frac{y _{1}^{0}}{y} $
$ v _{iy}=-( \frac{10}{x-10} )\frac{dy}{dt};v _{iy}=-18 $
$ {{\vec{v}} _{image,mirror}}=-16\hat{i}-18\hat{j};{{\vec{v}} _{image}}=-12\hat{i}-16\hat{j} $
$ |v|=20cm/s $
