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

To solve this problem, we need to use the lens formula and the concept of the power of lenses. The given problem involves a combination of a concave lens and a convex lens that together act as a convex lens.

Let's start by understanding the situation:

• The focal length of the convex lens is given as \(f_1 = 20\,\text{cm}\).
• The combination of lenses acts as a convex lens with focal length \(F = 50\,\text{cm}\).
• We need to find the power of the concave lens.

First, we need to calculate the power of the convex lens. The power \(P\) of a lens is given by the formula:

\(P = \frac{1}{f} \, \text{(in meters)}\)

Therefore, the power of the convex lens is:

\(P_1 = \frac{1}{0.20} = 5\,\text{D}\)

Since the combination acts as a convex lens with a focal length of \(50\) cm, its power is:

\(P = \frac{1}{0.50} = 2\,\text{D}\)

Now applying the formula for the combination of two lenses in contact:

\(P = P_1 + P_2\)

Where \(P_2\) is the power of the concave lens. Substituting the known values:

\(2 = 5 + P_2\)

Solving for \(P_2\):

\(P_2 = 2 - 5 = -3\,\text{D}\)

Thus, the power of the concave lens is \(-3.0\,D\).

Therefore, the correct answer is: 
\(P = -3.0\,D\)