Question

A convex lens of focal length $20 \text{ cm}$ is placed in contact with a concave lens of focal length $40 \text{ cm}$. The power of the combination is

• A. $+2.5 \text{ D}$
• B. $-2.5 \text{ D}$
• C. $+5 \text{ D}$
• D. $-5 \text{ D}$

Hint:

Remember that when combining lens powers, you simply add them together. The sign of each individual power indicates whether the lens is convex or concave.

Answer 1

The Correct Option is A

Step 1: Recall the power of a lens.
The power of a lens is the inverse of its focal length in meters. \[ P = \frac{1}{f} \] A convex lens has positive power and a concave lens has negative power.

Step 2: Convert the focal lengths.
The convex lens has $f_1 = 20$ cm $= 0.2$ m. The concave lens has $f_2 = -40$ cm $= -0.4$ m, negative because it is diverging.

Step 3: Find each power.
For the convex lens, \[ P_1 = \frac{1}{0.2} = +5 \text{ D} \] For the concave lens, \[ P_2 = \frac{1}{-0.4} = -2.5 \text{ D} \]

Step 4: Add the powers.
When lenses touch, the total power is the sum. \[ P = P_1 + P_2 = 5 + (-2.5) \]

Step 5: Simplify.
\[ P = +2.5 \text{ D} \] The combination is positive, so it behaves like a weak converging lens.

Step 6: State the answer.
The power of the combination is plus two point five diopters, which is option (1). \[ \boxed{P = +2.5 \text{ D}} \]