Optics 3 Question 20
20. A hollow double concave lens is made of very thin transparent material. It can be filled with air or either of two liquids $L _1$ or $L _2$ having refracting indices $n _1$ and $n _2$ respectively $\left(n _2>n _1>1\right)$. The lens will diverge a parallel beam of light if it is filled with
$(2000,2 M)$
(a) air and placed in air
(b) air and immersed in $L _1$
(c) $L _1$ and immersed in $L _2$
(d) $L _2$ and immersed in $L _1$
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Answer:
Correct Answer: 20. (d)
Solution:
- The lens makers’ formula is
$$ \frac{1}{f}=\frac{n _L}{n _m}-1 \quad \frac{1}{R _1}-\frac{1}{R _2} $$
where, $n _L=$ Refractive index of lens and
$$ n _m=\text { Refractive index of medium. } $$
In case of double concave lens, $R _1$ is negative and $R _2$ is positive. Therefore, $\frac{1}{R _1}-\frac{1}{R _2}$ will be negative.
For the lens to be diverging in nature, focal length $f$ should be negative or $\frac{n _L}{n _m}-1$ should be positive or $n _L>n _m$ but since $n _2>n _1$ (given), therefore the lens should be filled with $L _2$ and immersed in $L _1$.
