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

Question

A convex lens is in contact with concave lens. The magnitude of the ratio of their focal length is 2/3. Their equivalent focal length is 30 cm. What are their individual focal lengths? (A) -75, 50 (B) -10, 15 (C) 75, 50 (D) -15, 10

Tardigrade Admin · Accepted Answer

Let focal length of convex lens is + f then focal length of concave lens would be -(3/2)f . From the given condition, (1/30)=(1/f)-(2/3 f)=(1/3 f) ∴ f=10 cm Therefore, focal length of convex lens = + 10 cm and that of concave lens = -15 cm.

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

-75, 50

-10, 15

75, 50

-15, 10

Let focal length of convex lens is + $f$ then focal length of concave lens would be $- \frac{3}{2} f$ .
From the given condition,
$\frac{1}{30} = \frac{1}{f} - \frac{2}{3 f} = \frac{1}{3 f}$
$∴ f = 10$ cm
Therefore, focal length of convex lens = + 10 cm and that of concave lens = -15 cm.

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

-75, 50

-10, 15

75, 50

-15, 10

Let focal length of convex lens is + f then focal length of concave lens would be −23​f . From the given condition, 301​=f1​−3f2​=3f1​ ∴f=10 cm Therefore, focal length of convex lens = + 10 cm and that of concave lens = -15 cm.

Let focal length of convex lens is + $f$ then focal length of concave lens would be $- \frac{3}{2} f$ .
From the given condition,
$\frac{1}{30} = \frac{1}{f} - \frac{2}{3 f} = \frac{1}{3 f}$
$∴ f = 10$ cm
Therefore, focal length of convex lens = + 10 cm and that of concave lens = -15 cm.