Question

A concave lens of focal length -18 cm is placed in contact with a convex lens of focal length +12 cm. The focal length of the combination will be:

• A. 36 cm
• B. -36 cm
• C. 48 cm
• D. -48 cm

Hint:

When combining two lenses in contact, the focal length of the combination is found by adding the reciprocals of the individual focal lengths. Remember that for a concave lens, the focal length is negative and for a convex lens, it is positive.

Answer 1

The Correct Option is A

We know the formula for the focal length of the combination of two lenses in contact: \[ \frac{1}{f_{\text{combination}}} = \frac{1}{f_1} + \frac{1}{f_2} \] where: - \( f_1 \) is the focal length of the first lens (concave lens, \( f_1 = -18 \, \text{cm} \)), - \( f_2 \) is the focal length of the second lens (convex lens, \( f_2 = +12 \, \text{cm} \)). Substituting the values: \[ \frac{1}{f_{\text{combination}}} = \frac{1}{-18} + \frac{1}{12} \] Let's calculate this: First, find the common denominator: \[ \frac{1}{f_{\text{combination}}} = \frac{-1}{18} + \frac{1}{12} = \frac{-2}{36} + \frac{3}{36} = \frac{1}{36} \] Therefore: \[ f_{\text{combination}} = 36 \, \text{cm} \] Thus, the focal length of the combination is 36 cm.