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) $-15,10$
Show Answer
Answer:
Correct Answer: 17. (d)
Solution:
- 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 $=-15 cm$
