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

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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 $



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