Question

A concave lens is kept in contact with a convex lens of focal length \(20\,cm\). The combination works as a convex lens of focal length \(50\,cm\). The power of concave lens is:

• A. \(P = -3.0\,D\)
• B. \(P = +3.0\,D\)
• C. \(P = -0.3\,D\)
• D. \(P = +0.3\,D\)

Hint:

Concave lens \(\Rightarrow\) negative focal length and power.

Answer 1

The Correct Option is A

Concept: \[ \frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2} \]

Step 1: Convert to meters.
\[ f_1 = 0.20\,m, \quad F = 0.50\,m \]

Step 2: Substitute.
\[ \frac{1}{0.50} = \frac{1}{0.20} + \frac{1}{f_2} \] \[ 2 = 5 + \frac{1}{f_2} \Rightarrow \frac{1}{f_2} = -3 \]

Step 3: Power.
\[ P = \frac{1}{f_2} = -3.0\,D \]