Question

O . 3) A diverging lens has f= -12 cm. A) Draw a ray diagram and find the image location and magnification for an object located 15 cm from the lens. B) Repeat for a converging lens of the same focal length (+12 cm).

Answer 1

Part a) - Solution

Using the thin lens equation, we can get the image distance

$\frac{1}{d_{obj}}+\frac{1}{d_{image}}=\frac{1}{f}$

11 1

$\Rightarrow \: \: \: \frac{1}{d_{image}}=\frac{d_{obj}-f}{fd_{obj}}$

$\Rightarrow \: \: \: d_{image}=\frac{fd_{obj} }{d_{obj}-f}$

$\Rightarrow \: \: \: d_{image}=\frac{(-12cm)(15cm) }{15cm-(-12cm)}$

or

${\color{Blue} d_{image}=-6.67cm}$

The magnification is

$M=-\frac{d_{image}}{d_{obj}}$

$\Rightarrow \: \: \: M=-\frac{(-6.67cm)}{15cm}$

or

${\color{Blue} M=0.445}$

Part b) - Solution

Using the thin lens equation, we get

$d_{image}=\frac{fd_{obj} }{d_{obj}-f}$

$\Rightarrow \: \: \: d_{image}=\frac{(+12cm)(15cm) }{15cm-(+12cm)}$

or

${\color{Blue} d_{image}=60 \, cm}$

The magnification is

$M=-\frac{d_{image}}{d_{obj}}$

$\Rightarrow \: \: \: M=-\frac{60cm}{15cm}$

or

${\color{Blue} M=-4}$

Ray diagrams rules for the thin lens can be found in the book "Physics for scientists, 7th edition. Page 1024, chapter 36"

Diverging lens Front 1 Back FI Converging lens Front Front Back Back 1