Optics 3 Question 13
13. The image of an object, formed by a plano-convex lens at a distance of $8 m$ behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is $2 / 3$ times the wavelength in free space. The radius of the curved surface of the lens is
(2013 Adv.)
(a) $1 m$
(b) $2 m$
(c) $3 m$
(d) $6 m$
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Answer:
Correct Answer: 13. (c)
Solution:
- $\mu=\frac{\lambda _{\text {air }}}{\lambda _{\text {medium }}}=\frac{1}{(2 / 3)}=\frac{3}{2}$
Further, $\quad|m|=\frac{1}{3}=\left|\frac{v}{u}\right|$
$\therefore \quad|v|=\frac{|u|}{3}$
$\Rightarrow \quad u=-24 m$ (Real object)
$\therefore \quad v=+8 m$ (Real image)
$$ \begin{aligned} & \text { Now, } \quad \frac{1}{v}-\frac{1}{u}=\frac{1}{f}=(\mu-1) \frac{1}{+R}-\frac{1}{\infty} \\ & \therefore \quad \frac{1}{8}+\frac{1}{24}=\frac{3}{2}-1 \frac{1}{R} \\ & \therefore \quad R=3 m \end{aligned} $$
