# Homework Help: Angular magnification

1. Feb 7, 2010

### EmmaK

1. The problem statement, all variables and given/known data
Conside two ways to use a convex lens (1) image formed at infinity s'=-$$\infty$$ and (2)s' at the near-point s'=-p_n. The angular magnifications are M_$$\infty$$ and M_pn respectively.
Derive the angular magnification M_pn and show that M_pn = M_$$\infty$$ + 1

2. Relevant equations
M_angular = $$\stackrel{\theta '}{\theta}$$

3. The attempt at a solution

I found the object distance for (2) to be $$\stackrel{fp_n}{f+p_n}$$

M_pn =$$\stackrel{y/s}{y/p_n}$$ =p_n /s = $$\stackrel{f+p_n}{f}$$

M_$$\infty$$ = $$\stackrel{y/f}{y/p_n}$$ =$$\stackrel{p_n}{f}$$

so M_$$\infty$$ +1 = $$\stackrel{p_n + f}{f}$$ =M_pn

so it worked out, but im unsure whether i put in $$\theta$$' and$$\theta$$ correctly for each case, as i didnt really understand what i was doing.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution