Question

To read a poster on a wall, a person with defective vision needs to stand at a distance of $0.4m$ from the poster. A person with normal vision can read the poster from a distance of $2.0m$. Which one of the following lens may be used to correct the defective vision?

• A. A concave lens of $0.5D$
• B. A concave lens of $1.0D$
• C. A concave lens of $2.0D$
• D. A convex lens of $2.0D$

Answer 1

Answer: (C)

A concave lens of $2.0D$

From the given problem, it is clear that the person can not see far objects. Therefore, he is suffering from hypermetropia. This defect can be corrected by using a concave lens of suitable power.

$\text{Calculating the power of the concave lens:}$

Given: the object distance $u=-2m$

the image distance $v=-0.4m$

Using the lens formula,
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$P=\frac{1}{f}=-\frac{1}{0.4}-\frac{1}{(-2)}=-2$
$P=-2D$
The power of the concave lens should be $2D$.