Optics Ques 183
- Diameter of a plano-convex lens is $6 $ $ cm$ and thickness at the centre is $3$ $ mm$. If speed of light in material of lens is $2 \times 10^{8}$ $m / s$, the focal length of the lens is
(2013 Main)
(a) $15 $ $cm$
(b) $20 $ $cm$
(c) $30 $ $cm$
(d) $10 $ $cm$
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Answer:
Correct Answer: 183.(c)
Solution:
Formula:
Refraction at Spherical Thin Lens:
- By Pythagoras theorem
$ R^{2}=(3)^{2}+(R-0.3)^{2} \Rightarrow R \approx 15 $ $cm $
Refractive index of material of lens $\mu=\frac{c}{v}$
Here $c=$ speed of light in vacuum $=3 \times 10^{8}$ $ m / s$
$v=$ speed of light in material of lens $=2 \times 10^{8}$ $ m / s$
$ =\frac{3 \times 10^{8}}{2 \times 10^{8}}=\frac{3}{2} $
From lens maker’s formula
$ \frac{1}{f}=(\mu-1) (\frac{1}{R _1}-\frac{1}{R _2}) $
Here, $R _1=R$ and $R _2=\infty$ (For plane surface)
$ \begin{aligned} \frac{1}{f}=(\frac{3}{2}-1) (\frac{1}{15}) \\ \Rightarrow f =30 cm \end{aligned} $
BETA
