Question

Consider the lens equation (1) for a convex (converging) lens. If you were to determine
where an image is formed for an object very, very far away, like the sun, an approximate
relationship between the image length and the focal point can be derived. By looking up the
distance from the earth to the sun to assist you, derive this relationship. Remember to
reference properly!

Answer 1

We know that the lens equation,

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

Now, as per the requirement of the question,

object is too far, it means we will consider as $u=\infty$

Now, we can write it as,

$\frac{1}{v}+\frac{1}{\infty}=\frac{1}{f}$

or we can write it as

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

Hence,

$v=f$

The formation of the long distant object will take place at the focal point of the lens.