Question

A convex lens of focal length 40 cm and a concave lens of focal length 20 cm are in contact. The power of their combination in dioptre is

• A. 2.5
• B. -2.5
• C. 7.5
• D. -7.5

Hint:

Always convert focal lengths to meters before calculating power in dioptres. Forgetting this conversion is a very common mistake. Also, be careful with the sign convention: convex is positive (+), concave is negative (-).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
When thin lenses are placed in contact, the power of the combination is the algebraic sum of the powers of the individual lenses. The power of a lens is defined as the reciprocal of its focal length in meters.
Step 2: Key Formula or Approach:
Power of a lens, \(P = \frac{1}{f(\text{in meters})}\). The unit of power is the dioptre (D).
For a combination of lenses in contact: \(P_{\text{combination}} = P_1 + P_2\).
Sign Convention: The focal length of a convex lens is positive, and the focal length of a concave lens is negative.
Step 3: Detailed Explanation:
Lens 1 (Convex):
Focal length, \(f_1 = +40\) cm = \(+0.4\) m.
Power, \(P_1 = \frac{1}{+0.4} = \frac{10}{4} = +2.5\) D.
Lens 2 (Concave):
Focal length, \(f_2 = -20\) cm = \(-0.2\) m.
Power, \(P_2 = \frac{1}{-0.2} = -\frac{10}{2} = -5.0\) D.
Power of the Combination:
Now, add the individual powers algebraically: \[ P_{\text{combination}} = P_1 + P_2 = (+2.5) + (-5.0) = -2.5 \, \text{D} \] Step 4: Final Answer:
The power of the combination is -2.5 dioptres. The negative sign indicates that the combination acts as a concave (diverging) lens. Option (B) is correct.