Chapter 23, Problem 58P

To determine

The locations of the lens having focal length 16 cm between object and the image seperated by 86 cm for which sharp images are created.

Answer to Problem 58P

Solution:

The distances are of the lens from object creating sharp images at 86 cm are 21.25 cm and 64.75 cm

Explanation of Solution

Formula used:

Lens equation, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

f, u and v are lens to focal, lens to object and lens to image distances repectively, negative when opposite to optical path and positive when in the direction of optical path.

Calculation:

As $\left|v\right|+\left|u\right|=86$ and $v=-u$

Thus,

We can write $u=-da\text{nd }v=86-d\text{ with }86>d>0$

Putting this in lens equation we get,

$\frac{1}{86-d}+\frac{1}{d}=\frac{1}{16}$ giving the quadratic equation-

$d^2-86d+86\times 16=0$

Two solutions to this equation are $d=21.25\text{ and }d=64.75$