Question

Assertion :A short-sighted person can not see objects clearly when placed beyond $50cm$. He should use a concave lens of power $2D$. Reason: The concave lens should form the image of the object at infinity at a distance of $50cm$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Given,

The far point of a normal eye $=50cm$

We know,

The far point of the normal eye $=\infty$

Object distance, $u=-\infty$

Image distance, $v=-50cm$

Focal length, $f$

Using lens formula,

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

$\frac{1}{f}=\frac{1}{-50}-\frac{1}{-\infty }$

$\frac{1}{f}=\frac{1}{-50}$

$f=-50cm=-0.5m$

$\therefore$ the lens use for correction should be concave lens

Power, $P=\frac{1}{f}$

$P=\frac{1}{-0.5}$

$P=-2D$

He should use a concave lens of power $2D$.

The concave lens should form the image of the object at infinity at a distance of $50cm$.