Ray Optics and Optical Instruments - Result Question 4

4. A rod of length $10 cm$ lies along the principal axis of a concave mirror of focal length $10 cm$ in such a way that its end closer to the pole is $20 cm$ away from the mirror. The length of the image is :

[2012M]

(a) $10 cm$

(b) $15 cm$

(c) $2.5 cm$

(d) $5 cm$

Show Answer

Answer:

Correct Answer: 4. (d)

Solution:

(d) According to the condition,

The focal length of the mirror

$-\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

For $A$ end of the rod the image distance When $u_1=-20 cm$

$\Rightarrow \frac{-1}{10}=\frac{1}{v_1}-\frac{1}{20}$

$\frac{1}{v_1}=\frac{-1}{10}+\frac{1}{20}=\frac{-2+1}{20}$

$v_1=-20 cm$

For when $u_2=-30 cm$

$\frac{1}{f}=\frac{1}{v_2}-\frac{1}{30}$

$\frac{1}{v_2}=\frac{-1}{10}+\frac{1}{30}=\frac{-30+10}{300}=\frac{-20}{300}$

$v_2=-15 cm$

$L=v_2-v_1=-15-(-20)$

$L=5 cm$