Question

A person cannot see the object clearly placed at a distance more than $40cm$. He is advised to use the lens of power.

• A. $-2.5D$
• B. $+2.5D$
• C. $-1.5D$
• D. $+1.5D$

Answer 1

The correct option is A

$-2.5D$

Step 1: Given data-

A person is unable to view beyond 40 cm.

Therefore to view far-off objects the lens required must be capable of producing the image of objects from infinity within $40cm$distance.

Step 2: Calculate the focal length of the required lens-

Here, $u=-\infty$and $v=-40cm$ Since the distance of both object and image is measured in opposite direction to the light ray direction, the distances are taken to be negative.

Using the lens equation,

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$$\begin{gathered} \Rightarrow \frac{1}{f}=-\frac{1}{40}-\frac{1}{(-\infty )} \\ \Rightarrow f=-40cm=-0.4m \end{gathered}$$

Step 3: Calculate the power of the lens-

We know that $P=\frac{I}{f}D$

$D$ stands for dioptre which is a unit of power.

Now,

$$\begin{gathered} P=-\frac{1}{0.4}D \\ P=-2.5D \end{gathered}$$

The negative sign in power indicates that a concave lens is used which is also clear by the fact that the person is nearsighted and such cases are resolved using a concave lens.

Thus, a person should use lens of power $-2.5D$.

Hence, option A is the correct answer.