Question

Find the power (with sign) of a concave of focal length $20\;{\text{cm}}$.

A. $- 4\;{\text{D}}$

B. $- 5\;{\text{D}}$

C. $4\;{\text{D}}$

D. $5\;{\text{D}}$

Answer 1

In this question, use the concept of the sign convention of the focal length of the concave lens that is the sign used for the concave lens for the focal length will be negative then use the formula of power of lens to find out the solution of given question.

Complete step by step answer:
From the given question we must find the power of a concave lens of focal length$20\;{\text{cm}}$. First, we must know about the definition of power, Power is defined as it is the reciprocal of focal length; whereas focal length of one meter is to one doper. Power of lens is represented by $P$.
Let us know about the focal length, focal length is an optical system to measure how strongly the system converges or diverges light. Focal length is the reciprocal of power and focal length is represented by $f$ the positive focal shows that the system converges light while negative focal length shows that the system diverges light.

We know that formula of power of lens is given as,
$P = \dfrac{1}{{f\left( {{\text{meter}}} \right)}}$
Where,
$P$ is power of lens and $f$ is the focal length in meters.
First, we convert the unit of focal length from centimeter to meter that is,
$f = 0.2\;{\text{m}}$
Because ${\text{1}}\;{\text{cm}} = 0.01\;{\text{meter}}$.

We know that according to the sign convention, the focal length will be negative for the concave lens.

On putting the values of focal length in the formula we find that,
$P = \dfrac{1}{{ - 0.2}}$
$\Rightarrow P = - 5\;{\text{D}}$

Therefore, the option B is correct.

Note: For calculating the power of a lens, always use the value of focal length in meters. Note that if the power of the lens is negative then the lens is a concave lens and if the power is positive then the lens is convex.