CBSE 2022 · Region 2 · Set 1 · Q7 · 3 marks
A converging lens made of glass $\displaystyle (\mu=1 \cdot 5)$ has its spherical faces of radii of curvature $\displaystyle 10$ cm and $\displaystyle 20$ cm. Find its focal length(a)in air, and(b)when it is immersed in a liquid of refractive index $\displaystyle 1$‧25.
A converging lens made of glass $\displaystyle (\mu=1 \cdot 5)$ has its spherical faces of radii of curvature $\displaystyle 10$ cm and $\displaystyle 20$ cm. Find its focal length
(a)
in air, and
(b)
when it is immersed in a liquid of refractive index $\displaystyle 1$‧25.
Marking-scheme solution
Finding the focal length
(a)
In Air
(b)
In Liquid
(a)
$$\frac{1}{\mathrm{f}_{\mathrm{a}}}=\left({ }_{\mathrm{a}} \mu^{\mathrm{g}}-$\displaystyle 1$\right)\left(\frac{1}{\mathrm{R}_{$\displaystyle 1$}}-\frac{1}{\mathrm{R}_{$\displaystyle 2$}}\right)
$$\mathrm{R}_{$\displaystyle 1$}=$\displaystyle 10$ \mathrm{~cm} & \mathrm{R}_{$\displaystyle 2$}=-$\displaystyle 20$ \mathrm{~cm},{ }_{\mathrm{a}} \mu^{\mathrm{g}}=$\displaystyle 1.5$
$$$\frac{1}{\mathrm{f}_{\mathrm{a}}}=(1.5-1)\left(\frac{1}{10}-\frac{1}{-20}\right)$
$$\mathrm{f}_{\mathrm{a}}=\frac{40}{3}=$\displaystyle 13.3$ \mathrm{~cm}
$$b) $\displaystyle \frac{1}{f_{l}}=\left({ }_{l} \mu^{g}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$
$$=\left(\frac{1.5}{1.25}-$\displaystyle 1$\right)\left(\frac{1}{10}-\frac{1}{-20}\right)
$$$f_{l}=\frac{100}{3}=33.3 \mathrm{~cm}$
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CBSE Class 12 Physics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.