Question

What should be the focal length of a lens to form a real point size image of a very far off object at a distance of 20cm from the lens?​

Answer 1

Answer:

The focal length of the lens = +20 cm.

Explanation:

The focal length of a lens is defined as the distance from the lens at which the light rays from infinity converge after refraction through the lens.

Also, the lens equations states that,

$\dfrac 1f=\dfrac 1v-\dfrac 1u$.

where,

• $f$ = focal length of the lens.

• $u$ = distance of the object from the lens.

• $v$ = distance of the image formed from the lens.

Given that object is very far away from the lens, such that,

$u>>v\\\therefore \dfrac 1u<<\dfrac 1v\\\Rightarrow \dfrac 1v-\dfrac 1u \approx \dfrac 1v$

Using lens equation,

$\dfrac 1f = \dfrac 1v-\dfrac 1u \approx \dfrac 1v\\\Rightarrow f=v=20\ cm.$.

Also, since the image formed is real and point sized which means the lens is convex, therefore the focal length should be positive too.

Thus, focal length of the lens = +20 cm.