Question

The power of the combination of two lenses made by keeping the convex lens of focal length 40 cm in contact with the concave lens of focal length 25 cm, is:

• A. -1.5 D
• B. -6.5 D
• C. +6.5 D
• D. +6.67 D

Hint:

For lenses in contact, simply add their powers algebraically to find the total power of the combination.

Answer 1

The Correct Option is A

The power \( P \) of a lens is given by the formula: \[ P = \frac{1}{f} \] where \( f \) is the focal length of the lens. For a combination of lenses in contact, the total power is the sum of the individual powers: \[ P_{\text{total}} = P_1 + P_2 \] where \( P_1 \) is the power of the convex lens and \( P_2 \) is the power of the concave lens. The power of the convex lens with focal length 40 cm is: \[ P_1 = \frac{1}{40 \, \text{cm}} = \frac{1}{0.4 \, \text{m}} = +2.5 \, \text{D} \] The power of the concave lens with focal length 25 cm is: \[ P_2 = \frac{1}{-0.25 \, \text{m}} = -4 \, \text{D} \] Thus, the total power is: \[ P_{\text{total}} = 2.5 \, \text{D} + (-4 \, \text{D}) = -1.5 \, \text{D} \] Therefore, the correct answer is (a).