Question

Two lenses, one of focal length 20 cm and another of power 4D are placed together, what is the effective power of the combination?

Hint:

When lenses are placed in contact, their total power is the sum of their individual powers.

Answer 1

Step 1: Use the formula for the power of a lens.
The power \( P \) of a lens is related to its focal length \( f \) by the formula: \[ P = \frac{1}{f} \] where \( f \) is the focal length in meters and \( P \) is in diopters (D).
Step 2: Convert the focal length to meters.
The focal length of the first lens is given as 20 cm. Convert this to meters: \[ f_1 = 20 \, \text{cm} = 0.2 \, \text{m} \] The power of the first lens is: \[ P_1 = \frac{1}{f_1} = \frac{1}{0.2} = 5 \, \text{D} \]
Step 3: Calculate the total power of the combination.
The total power of the combination of two lenses in contact is the sum of the individual powers: \[ P_{\text{total}} = P_1 + P_2 \] where \( P_2 = 4 \, \text{D} \) is the power of the second lens. Thus, the total power is: \[ P_{\text{total}} = 5 \, \text{D} + 4 \, \text{D} = 9 \, \text{D} \] Therefore, the effective power of the combination is: \[ \boxed{9 \, \text{D}} \]