Optics 3 Question 17

17. A convex lens is in contact with concave lens. The magnitude of the ratio of their focal length is $\frac{3}{2}$. Their equivalent focal length is $30 cm$. What are their individual focal lengths?

(2005, 2M)

(a) $-75,50$

(b) $-10,15$

(c) 75,50

(d) $-15,10$

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Answer:

Correct Answer: 17. (d)

Solution:

  1. Let focal length of convex lens is $+f$, then focal length of concave lens would be $-\frac{3}{2} f$.

From the given condition,

$$ \begin{aligned} \therefore \quad \frac{1}{30}=\frac{1}{f}-\frac{2}{3 f} & =\frac{1}{3 f} \\ f & =10 cm \end{aligned} $$

Therefore, focal length of convex lens $=+10 cm$ and that of concave lens $=-15 cm$



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