The Notes: A lens forms an image 15 cm away. The object is located 10 cm from the lens. What is the focal length of lens? What type of lens is it?

Friday, July 16, 2010

To solve, apply the thin lens equation.

$\displaystyle\frac{{1}}{{f{=}}}\frac{{1}}{{d}_{{o}}}+\frac{{1}}{{d}_{{i}}}$

where

f = len's focal length

$\displaystyle{d}_{{o}}$ = object distance

$\displaystyle{d}_{{i}}$ = image distance

Plugging in the given values, the formula becomes:

$\displaystyle\frac{{1}}{{f{=}}}\frac{{1}}{{10}}+\frac{{1}}{{15}}$

$\displaystyle\frac{{1}}{{f{=}}}\frac{{1}}{{10}}\cdot\frac{{3}}{{3}}+\frac{{1}}{{15}}\cdot\frac{{2}}{{2}}$

$\displaystyle\frac{{1}}{{f{=}}}\frac{{3}}{{30}}+\frac{{2}}{{30}}$

$\displaystyle\frac{{1}}{{f{=}}}\frac{{5}}{{30}}$

$\displaystyle\frac{{1}}{{f{=}}}\frac{{1}}{{6}}$

$\displaystyle{f{=}}{6}$

Therefore, the focal length of the lens is 6 cm.

Take note that a converging lens has a positive value for f. And a diverging lens has a negative value for f.

Since the resulting value of f is positive, then, the it is a converging lens.

The Notes