Question

The power of a lens is negative. State whether it is convex or concave?
A. Concave
B. Convex
C. Both A and B
D. Cannot be determined

Answer 1

Hint: We know that the power of a lens is defined as the reciprocal of the focal length. Lens power is measured in diopters. Converging lenses have positive focal lengths, so they also have positive power values. Diverging lenses have negative focal lengths, so they also have negative power values.

Complete step by step solution:
We know that
The power of a lens is defined as the power of a lens is defined as the reciprocal of the focal length.
According to definition we have,
$p={\displaystyle \frac{1}{f}}$, Where $p$ and $f$ stands for power and focal length of the lens respectively.
Concave lens with a virtual focus has negative focal length and hence, negative power.
Lenses bend light that passes through them. The direction and amount that the light bends depends on the curvature of the lens, the material the lens is made of, and the material in which the lens is immersed. If both sides of the lens curve outward, it is called a converging lens, and it will bend light from distant objects inwards toward a single point, called the focal point.
If both sides of the lens curve inward, it is called a diverging lens, and light from distant objects will bend outwards. Because the light is not being bent toward a single point, the focal point is not as obvious as it was in the case of the converging lens. We have to take the bent rays, and follow them back to the side of the lens that the light came from to make them come together and find the focal point. That means that the focal point is on the same side of the lens as the light rays were coming from.
Convex lenses have real focus while concave lenses have virtual focus hence the focal length is positive and negative for convex and concave lenses respectively.

$\therefore$ The power of the concave lens is negative. Hence the correct option is (A).

Note:
In actuality, there are two focal points for every lens, the same distance from the lens, on opposite sides. The distance from the lens to the focal point is called the focal length. For converging lenses, the focal length is always positive, while diverging lenses always have negative focal lengths. However, these conventions are arbitrary, and physicists could just as easily have made the signs opposite.