Chapter 25, Problem 8P

To determine

To show that focal length of a camera lens is proportional to focal length.

Answer to Problem 8P

Solution:

The focal length of a camera lens is proportional to focal length if the object is at infinity.

Explanation of Solution

Magnification is defined as, $magnification=\frac{\text{ image distance }}{\text{object distance}}$

i.e. $m=\frac{v}{u}$

From lens formula, $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

Given u = ∞, $\therefore \frac{1}{f}=\frac{1}{\infty }+\frac{1}{v}$$f=v$

$\therefore m=\frac{v}{u}=\frac{f}{u}$

$\therefore m\text{ α }f$