Question

PIUDICI
A person with myopia can see objects placed at
a distance of 4m. If he wants to see objects at a
distance of 20m, what should be the focal length
and power of the concave lens he must wear?​

Answer 1

QUESTION :-

A person with myopia can see objects placed at a distance of 4 m. If he wants to see objects at a distance of 20 m, what should be the focal length of the power concave lens he must wear​.

$\rule{200}5$

SOLUTION :-

It is given that,

• x = 4 m.

• y = 20 m.

We know, for a myopic eye,

$\boxed{\sf{\dag\ Focal\ length=\frac{xy}{x-y} }}$

Putting the values :-

$\sf{f=\dfrac{20 \times 4}{4-20} }\\\\\sf{\implies f=\dfrac{80}{-16} }\\\\\boxed{\sf{\implies f=-5\ m }}$

$\rule{100}1$

We also know,

Power = reciprocal of the focal length = 1/f

⇒Power = 1/-5

⇒Power = -0.2 Dioptre

Hence, the power of the concave lens must be -0.2 D that the person must wear.