Question

If two thin lenses with focal lengths of +10 cm and +20 cm are placed in contact, what is the total power of the combination?

• A. 10 D
• B. 5 D
• C. 15 D
• D. 30 D

Hint:

Remember to always convert focal lengths to meters (or use the $100/f$ formula for cm) before calculating Power. Power is additive only for thin lenses in contact.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need to find the total power of a lens combination when two thin converging (convex) lenses are placed in direct contact.
Step 2: Key Formula or Approach:
The power $P$ of a single lens in Diopters (D) is given by $P = \frac{100}{f}$, where $f$ is the focal length in centimeters.
When thin lenses are placed in contact, their equivalent power is simply the algebraic sum of their individual powers: \[ P_{\text{total}} = P_1 + P_2 \] Step 3: Detailed Explanation:
First, calculate the power of the first lens ($f_1 = +10 \text{ cm}$): \[ P_1 = \frac{100}{10} = +10 \text{ D} \] Next, calculate the power of the second lens ($f_2 = +20 \text{ cm}$): \[ P_2 = \frac{100}{20} = +5 \text{ D} \] Now, find the total power of the combination: \[ P_{\text{total}} = P_1 + P_2 = 10 \text{ D} + 5 \text{ D} = 15 \text{ D} \] Step 4: Final Answer:
The total power of the combination is $15 \text{ D}$.