Question

Two convex lenses of different focal lengths are in contact with each other. If the focal length of each lens is doubled, the focal power of the combination

• A. does not change
• B. is doubled
• C. is halved
• D. is tripled

Hint:

Since power is inversely proportional to focal length, doubling the focal length results in halving the power, whether it is for a single lens or a combination.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The total focal power (\(P\)) of a combination of lenses in contact is the algebraic sum of their individual powers.
Power is the reciprocal of the focal length (\(P = 1/f\)).

Step 2: Key Formula or Approach:
\(P_{comb} = P_1 + P_2 = \frac{1}{f_1} + \frac{1}{f_2}\)

Step 3: Detailed Explanation:
Let the initial focal lengths be \(f_1\) and \(f_2\).
Initial power \(P_{initial} = \frac{1}{f_1} + \frac{1}{f_2}\)
If both focal lengths are doubled:
\(f_1' = 2f_1\) and \(f_2' = 2f_2\)
New power \(P_{new} = \frac{1}{2f_1} + \frac{1}{2f_2} = \frac{1}{2} \left( \frac{1}{f_1} + \frac{1}{f_2} \right)\)
\[ P_{new} = \frac{1}{2} P_{initial} \]
Thus, the focal power is halved.

Step 4: Final Answer:
The focal power of the combination is halved.