Question

If the power of a lens is -2.0 D, then the type and focal length \( f \) of the lens are:

• A. Convex lens, 40 cm
• B. Concave lens, 50 cm
• C. Convex lens, 25 cm
• D. Concave lens, 20 cm
• E. Convex lens, 30 cm

Hint:

A negative power indicates a concave lens, and the focal length is negative for concave lenses. The relationship \( P = \frac{1}{f} \) allows you to easily calculate the focal length from the power.

Answer 1

The Correct Option is B

The power \( P \) of a lens is related to its focal length \( f \) by the equation: \[ P = \frac{1}{f} \] where: - \( P \) is the power of the lens in diopters (D),
- \( f \) is the focal length of the lens in meters.
We are given that the power of the lens is \( P = -2.0 \, {D} \). 
The negative sign indicates that the lens is a concave lens (since concave lenses have negative focal lengths).
Using the formula for power: \[ P = \frac{1}{f} \] Substitute the value of \( P \): \[ -2.0 = \frac{1}{f} \] Solving for \( f \): \[ f = \frac{1}{-2.0} = -0.5 \, {m} = -50 \, {cm} \] Thus, the focal length of the lens is \( -50 \, {cm} \), and since the focal length is negative, the lens is a concave lens.
Therefore, the correct answer is: \[ \boxed{{B) Concave lens, 50 cm}} \]