Question

The focal length of a concave lens is 2m. Then the power of the lens is
A. 2 dioptre
B. -2 dioptre
C. 0.5 dioptre
D. -0.5 dioptre

Answer 1

Hint: Power of lens is a measurement of the degree of convergence or divergence of the light falling on the lens. This question is solved by using the given focal length of the lens in the power lens formula.

Formula used: power of lens, P = $\dfrac{1}{f}$

Complete step by step answer:
The power of the lens is defined as the reciprocal of the focal length of the lens. And given by formula, $P=\dfrac{1}{f}$

Where, ‘f’ is the focal distance of the lens. When a parallel beam of light source is incident on a spherical mirror, the actual point where the reflected rays converge or appear to diverge from the purpose on the principal axis is called the principal focus. The distance between the pole and the principal focus is called the focal length (f) of the lens.

The given focal length of the concave lens is f = -2 m. It is negative because a concave lens always has a negative focal length.

Now, let us substitute ‘f’ in the lens power formula. We get,

$P=\dfrac{1}{f}=\dfrac{1}{-2}$
On solving, P = -0.5 dioptre
The unit of power is dioptre (D) and 1D = 1m^-1.
Therefore, the correct answer for the given question is option (D).

Note: The power of the lens is said to be 1 dioptre if the focal length of the lens is 1metre. That means, if the corrective power of the lens is +0.5D, the required lens is a convex lens of focal length +2m. In the same way, a power of -2.0D means a concave lens of focal length -0.5m.