Mirrors and Lenses Summary
| |
f = R/2 |
s' |
Image |
| Concave Mirror |
f > 0 |
s' > 0 |
real |
front |
inverted |
| s' < 0 |
virtual |
back |
upright |
| Convex Mirror |
f < 0 |
s' < 0 |
virtual |
back |
upright |
| Converging Lens |
f > 0 |
s' > 0 |
real |
back |
inverted |
| Diverging Lens |
f < 0 |
s' < 0 |
virtual |
front |
upright |
|
13.1: Spherical Mirror
***keep everything in cm***
s = x coordinate (positive)
f = R/2 (negative)
s' = (sf)/(s-f) [from 1/s + 1/s' = 1/f]
m = -s' / s
yimage = m*yobject [yobject is the y coordinate. it keeps its sign]
13.2: Plane Mirror
a) d = H1/2
b) hmin = H/2
c) distance D from the mirror is independent, therefore
hmin = H/2
d) s = 3H / 4
e) no part will be cut off, therefore
delta.H = 0
13.3: Two Lens System
do1 = the original object's distance from the first lens
f1 = the focal length of the first lens
di1 = the intermediate image of the original object through the first lens (measured from the first lens)
do2 = the intermediate image distance from the second lens (the object distance for the second lens)
f2 = the focal length of the second lens
di2 = the final image distance from the second lens
------------------------
di1 = do1f1/(do1-f1) where do1 = X1
f2 = do2di2/(do2+di2) where do2 = X2 - di1 and di2 = X3
13.4: Double Concave Lens
a) P = 1/f = (n-1)(-1/Rl - 1/Rr)
b) 1/d + 1/s1' = 1/f where 1/f = P
~ s1' = d/(Pd-1) [note: the P above is in meters, this answer wants cm]
c) H' = H*(-s1'/d)
d) 2 - Virtual
e) 11 - Upright
f) -1/d + 1/s2' = 1/f
~ s2' = d/(Pd+1) [note: the P above is in meters, this answer wants cm]
g) 1 - Real
h) 11 - Upright
i) 111 - Right