Optics 1 Question 9
9. A short linear object of length $b$ 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
(a) $b \frac{u-f^{1 / 2}}{f}$
(b) $b \frac{f}{u-f}$
(c) $b \frac{u-f}{f}$
(d) $b \frac{f^{2}}{u-f}$
Assertion and Reason
Mark your answer as
(a) If Statement I is true, Statement II is true; Statement II is the correct explanation for Statement I.
(b) If Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I.
(d) If Statement I is false; Statement II is true.
Show Answer
Answer:
Correct Answer: 9. (d)
Solution:
- From the mirror formula
$$ \begin{aligned} \frac{1}{v}+\frac{1}{u} & =\frac{1}{f} \quad(f=\text { constant }) \\ -v^{-2} d v-u^{-2} d u & =0 \\ |d v| & =\frac{v^{2}}{u^{2}}|d u| \end{aligned} $$
Here, $|d v|=$ size of image
$|d u|=$ size of object (short) lying along the axis $=b$
Further, from Eq. (i), we can find
$$ \frac{v^{2}}{u^{2}}=\frac{f}{u-f} $$
Substituting these values in Eq. (ii), we get
Size of image $=b \frac{f}{u-f}$
$\therefore$ Correct option is (d).
