A convex lens is in contact with a concave lens. The magnitude of the ratio of their focal lengths is 2/3. Their equivalent focal length is 30 cm. What are their individual focal lengths? [2005]

Question

A convex lens is in contact with a concave lens. The magnitude of the ratio of their focal lengths is 2/3. Their equivalent focal length is 30 cm. What are their individual focal lengths? [2005]

Smart Achievers · Accepted Answer

(1)

Focal length of concave lens, $f_{2} = - \frac{3}{2} f_{1}$

$f_{1} =$ focal length of the convex lens.

$\frac{1}{f} = \frac{1}{f_{1}} - \frac{1}{f_{2}}$ $\Rightarrow \frac{1}{30} = \frac{1}{f_{1}} - \frac{2}{3 f_{1}}$

$∴$ $f_{1} = 10 cm$ and $f_{2} = - \frac{3}{2} \times 10 = - 15 cm$

Solution

Q.
A convex lens is in contact with a concave lens. The magnitude of the ratio of their focal lengths is 2/3. Their equivalent focal length is 30 cm. What are their individual focal lengths [2005]

1 −15, 10

2 −10, 15

3 75, 50

4 −75, 50

Ans.
(1)

Focal length of concave lens, $f_{2} = - \frac{3}{2} f_{1}$

$f_{1} =$ focal length of the convex lens.

$\frac{1}{f} = \frac{1}{f_{1}} - \frac{1}{f_{2}}$ $\Rightarrow \frac{1}{30} = \frac{1}{f_{1}} - \frac{2}{3 f_{1}}$

$∴$ $f_{1} = 10 cm$ and $f_{2} = - \frac{3}{2} \times 10 = - 15 cm$

Want Us to Email you About Special Offers & Updates?