A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm, respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid-glass combinatio

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Solution

Q.
A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm, respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid-glass combination will be [2025]

1 $\frac{500}{11} cm$

2 $\frac{800}{11} cm$

3 $\frac{700}{11} cm$

4 $\frac{600}{11} cm$

Ans.
(4)

$\frac{1}{f} = (1.3 - 1) (\frac{1}{\infty} - \frac{1}{- 30}) + (1.5 - 1) (\frac{1}{- 30} - \frac{1}{- 20})$

$= \frac{0.3}{30} + \frac{0.5}{60} = \frac{6 + 5}{600} = \frac{11}{600}$

$\Rightarrow f = \frac{600}{11} cm$

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