Chapter 25, Problem 5P

To determine

The object distance and the distance between object and image on the film.

Answer to Problem 5P

Solution:

The object distance is 110mm, and the distance between object and image on the film is 220mm.

Explanation of Solution

By using magnification formula and lens formula, the object distance can be calculated.

Given:

Focal length $f=\text{55mm}$, height of the object = height of the image $\left(h_o=h_i\right).$

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:

Since $h_o=h$ magnification, $m=\frac{h_i}{h_o}=\frac{v}{u}=1$, $\therefore u=v$

From lens formula, $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}=\frac{1}{u}+\frac{1}{u}=\frac{2}{u}$

$\therefore u=2f=2\times 55=110\text{mm}$

And distance between object and image $=u+v=u+u=2u=2\times 110=220\text{mm}$