- #1

Baal Hadad

- 17

- 2

- Homework Statement
- Given the diagram below, I would like to derive the expression for linear magnification:

- Relevant Equations
- $$m=\mod{\frac{n_1v }{n_2u}}$$

I tried assumed ##\theta \approx sin \theta \approx tan \theta##.

By Snell's law(after approximation),

$$n_1 \tan( i_1)= n_2 \tan( i_2)$$

If ##\tan (i_1)=\frac {h_o}{ u}## and ##\tan (i_2)=\frac {h_i}{ v}##,then

$$m=\frac {h_i}{h_o}=\mod{\frac {v n_1}{un_2}}$$

Which is the expected expression.

I don't consider orientation of image here.

The point that I confused is why##\tan (i_1)=\frac {h_o}{ u}## and ##\tan (i_2)=\frac {h_i}{ u}##.

I even can't find the height of image and object from this diagram,and how the height is related with the angle ##i_1## and ##i_2##.

Can anyone help me?

Thanks in advance.

By Snell's law(after approximation),

$$n_1 \tan( i_1)= n_2 \tan( i_2)$$

If ##\tan (i_1)=\frac {h_o}{ u}## and ##\tan (i_2)=\frac {h_i}{ v}##,then

$$m=\frac {h_i}{h_o}=\mod{\frac {v n_1}{un_2}}$$

Which is the expected expression.

I don't consider orientation of image here.

The point that I confused is why##\tan (i_1)=\frac {h_o}{ u}## and ##\tan (i_2)=\frac {h_i}{ u}##.

I even can't find the height of image and object from this diagram,and how the height is related with the angle ##i_1## and ##i_2##.

Can anyone help me?

Thanks in advance.