Optics Question 81
Question: A short linear object of length $ l $ lies along the axis of a concave mirror of focal length f at a distance $ u $ from the pole of the mirror. The size of the image is approximately equal to
[IIT-JEE 1988; BHU 2003; CPMT 2004]
Options:
A) $ l{{( \frac{u-f}{f} )}^{1/2}} $
B) $ l{{( \frac{u-f}{f} )}^{2}} $
C) $ l{{( \frac{f}{u-f} )}^{1/2}} $
D) $ l{{( \frac{f}{u-f} )}^{2}} $
Show Answer
Answer:
Correct Answer: D
Solution:
From mirror formula $ \frac{1}{f}=\frac{1}{v}+\frac{1}{u} $ …..(i)
Differentiating equation (i), we obtain $ 0=-\frac{1}{v^{2}}dv-\frac{1}{u^{2}}du $
$ \Rightarrow dv=-{{( \frac{v}{u} )}^{2}}du $ …..(ii)
Also from equation (i) $ \frac{v}{u}=\frac{f}{u-f} $ …..(iii)
From equation (ii) and (iii) we get $ dv=-{{( \frac{f}{u-f} )}^{2}}.\ l $
Therefore size of image is $ {{( \frac{f}{u-f} )}^{2}}l. $
