Question

A convex lens of focal length $ f = 20 \, \text{cm} $ is combined with a diverging lens of power 65 D. The power and the focal length of the combination is

• A. -1.5 D, 66.7 cm
• B. 1.5 D, 33.7 cm
• C. 5 D, 66.7 cm
• D. 5 D, 33.6 cm

Hint:

When combining lenses, the total power is the sum of the individual powers, and the total focal length is the inverse of the total power.

Answer 1

The Correct Option is C

Step 1: Power of the convex lens.
The power \( P \) of a lens is given by the formula: \[ P = \frac{1}{f} \] where \( f \) is the focal length in meters.
For the convex lens, \[ P_{\text{convex}} = \frac{1}{0.2} = 5 \, \text{D} \]
Step 2: Power of the diverging lens.
The power of the diverging lens is already given as \( P_{\text{divergent}} = -65 \, \text{D} \) (negative because it is a diverging lens).
Step 3: Total power of the combination.
The total power of the lens combination is the sum of the individual powers: \[ P_{\text{total}} = P_{\text{convex}} + P_{\text{divergent}} = 5 \, \text{D} + (-65 \, \text{D}) = -1.5 \, \text{D} \]
Step 4: Focal length of the combination.
The focal length \( f_{\text{total}} \) of the combination is related to the total power by the formula: \[ f_{\text{total}} = \frac{1}{P_{\text{total}}} \] Substituting the total power: \[ f_{\text{total}} = \frac{1}{-1.5 \, \text{D}} = -66.7 \, \text{cm} \]