- #1
EmmaK
- 26
- 0
Homework Statement
Conside two ways to use a convex lens (1) image formed at infinity s'=-[tex]\infty[/tex] and (2)s' at the near-point s'=-p_n. The angular magnifications are M_[tex]\infty[/tex] and M_pn respectively.
Derive the angular magnification M_pn and show that M_pn = M_[tex]\infty[/tex] + 1
Homework Equations
M_angular = [tex]\stackrel{\theta '}{\theta}[/tex]
The Attempt at a Solution
I found the object distance for (2) to be [tex]\stackrel{fp_n}{f+p_n}[/tex]
M_pn =[tex]\stackrel{y/s}{y/p_n}[/tex] =p_n /s = [tex]\stackrel{f+p_n}{f}[/tex]
M_[tex]\infty[/tex] = [tex]\stackrel{y/f}{y/p_n}[/tex] =[tex]\stackrel{p_n}{f}[/tex]
so M_[tex]\infty[/tex] +1 = [tex]\stackrel{p_n + f}{f}[/tex] =M_pn
so it worked out, but I am unsure whether i put in [tex]\theta[/tex]' and[tex]\theta[/tex] correctly for each case, as i didnt really understand what i was doing.