Chapter 25, Problem 6P

To determine

The focal length of the lens used in the camera.

Answer to Problem 6P

Solution:

The focal length of the lens used in the camera should be 46mm.

Explanation of Solution

By using magnification formula and lens formula, the focal length can be calculated.

Given:

Height of the object $h_o=\text{ 34m}$, height of the image $h_i=\text{ 24m}$ mm, object distance $u=\text{ 65m}$

Formula used:

$magnification=\frac{\text{height of the image }}{\text{height of the object}}=\frac{\text{ image distance }}{\text{object distance}}$

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

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

Calculation:

Magnification, $m=\frac{h_i}{h_o}=\frac{v}{u}$

$v=\frac{h_i}{h_o}u=\frac{24\times {10}^{-3}}{34}\times 65=45.88\times {10}^{-3}m=45.88mm$

From lens formula,

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

$\frac{1}{f}=\frac{1}{65}+\frac{1}{45.88\times {10}^{-3}}=21.94$

$f=\frac{1}{21.94}=0.0455m=45.5\text{mm;46mm}$