Answer to Question #140780 in Optics for kgokane

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

From the lens equation we know that;

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

As per the conditions of the question,

the object is too far hence we will consider $u=∞$

in this case we rewrite the equation as ;

$\frac{1}{v}+\frac{1}{∞}=\frac{1}{f}$

or

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

therefore, $v=f$

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