Question

A far sighted person can see object beyond 71 cm clearly if separation between glasses and eye lens is 2 cm, then find focal length of glass?

• A. 23 cm
• B. 34.5 cm
• C. 18.4 cm
• D. 30 cm

Answer 1

The correct option is B 34.5 cm

Complete step by step answer:

We have given that the person can see beyond 71 cm clearly that means for the object placed at distance of distinct vision (25 cm), the image should be formed at 71 cm from the eye. We have given the separation between glasses and eye lens is d=2cm.

Therefore, the object distance from the lens is,

$u=-(25-2)=-23cm$

And the image distance is,

$v=-(71-2)=-69cm$

We have the lens formula relating focal length, image distance and object distance,

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

Substituting $u=-23cm$

and $v=-69cm$

in the above equation, we get,

$\frac{1}{f}=\frac{-1}{69}+\frac{1}{23}$

⇒$f=\frac{69}{2}$

$\therefore f=34.5cm$

Since the focal length is positive, the lens that the person is using is the convex lens.

So, the correct answer is option B.

Note:Do not take the image distance as 71 cm since it is the distance between the eye lens and the image. The image distance and object distance should be taken from the pole of the lens. The distance of distinct vision is 25 cm and it is always negative.