Question

Two thin lenses are in contact and the focal length of the combination is 80 cm. If the focal length of one lens is 20 cm, then the power of the other lens will be:

• A. 1.66D
• B. 4.00D
• C. -100D
• D. -3.75D

Hint:

For lenses in contact, their total power is the sum of their individual powers.

Answer 1

The Correct Option is B

Step 1: Lens formula.
The power of a lens is given by: \[ P = \frac{1}{f} \] where \( f \) is the focal length. The total power \( P_{\text{total}} \) of two lenses in contact is the sum of their individual powers: \[ P_{\text{total}} = P_1 + P_2 \] Step 2: Power of the lenses.
Given the focal length of the combination \( f_{\text{total}} = 80 \, \text{cm} \), the power of the combination is: \[ P_{\text{total}} = \frac{1}{f_{\text{total}}} = \frac{1}{0.80} = 1.25 \, \text{D} \] The power of the first lens is: \[ P_1 = \frac{1}{f_1} = \frac{1}{20} = 5 \, \text{D} \] Thus, the power of the second lens is: \[ P_2 = P_{\text{total}} - P_1 = 1.25 - 5 = 4.00 \, \text{D} \]
Final Answer: \[ \boxed{4.00 \, \text{D}} \]