BHS 120.1 – Optics I
Notetaker: Lara Match
Date: 10/09/2012, 1st hour
Page#
Practice Problem #11 should say the opposite lens shape as it does
SRS FORMULAS
SRS Formula
P = (n’ – n) / r
P = (n’ / l’) – (n / l)
P = L’ – L
(because L’ = n’ / l’ and L = n / l)
Formula modified for PPF, light coming from infinity
f’ = secondary focal length associated with PPF
f’ = l’ when object at infinity
Substituting equations when object at infinity (n / ∞)
n’ / f’ = P
Formula modified for APF, light heading towards infinity
f = l when light heading towards infinity
f = primary focal length associated with APF
Substituting equations when image at infinity (n’ / ∞)
-n / f = P
f + f’ = r
Four SRS set-ups
1.
2.
3.
4.
+ r, n’ > n = convergent, real (-) APF, real (+) PPF
+ r, n > n’ = divergent, virtual (+) APF, virtual (-) PPF
– r, n’ > n = divergent, virtual (+) APF, virtual (-) PPF
– r, n > n’ = convergent, real (-) APF, real (+) PPF
Tips/Reminders
Get through these conceptual steps quickly on exams because there will be plenty more to figure out
Even for virtual APF and PPF, you must use n for APF and n’ for PPF, never the other way around
RAY DIAGRAMS
Label APF, PPF and then two points further out along the optic axis 2*PPF and 2*APF
Your actual numbers may change, but the patterns of image size and inversion will not
Refresh object Vergence
L = 1.00 / l, taking reciprocal works if medium is air
L = n / l, truly it is the index of refraction over the object distance
l must be in meters
Refresh object/image location
- Real object = anterior to lens (- distance) L = n / l
- Real image = posterior to lens (+ distance) L’ = n’ / l’
- Virtual object = posterior to lens (+ distance) L = n / l
- Virtual image = anterior to lens (- distance) L’ = n’ / l’
BHS 120.1 – Optics I
Notetaker: Lara Match
Date: 10/09/2012, 1st hour
Page#
Recall Reduced Vergence
The closer the values of n and n’ are to each other, the weaker the functional power of the lens
The larger the difference between n and n’, the stronger the power
MAGNIFICATION
M = L / L’
A measure that is the ratio of object to image size
Lateral Magnification = h’ / h
Ratio < 1 = magnification
Ratio > 1 = minification
Vergence = object / image
Magnification = image/object
SET UP for SRS OBJECT-IMAGE PATTERNS
GIVEN
Real object
h = 2cm
l = - 100cm
convex so r is (+)
air to CR39
n = 1.00
n’ = 1.50
rare to dense (+)r, will
converge light, APF(-) and
PPF(+) will be real
P = (n’ – n) /r = +5.00D
f’ = n’ / P = +30cm
f = -n / P = -20cm
APF = -20cm
2APF = -40cm
PPF = +30cm
2PPF = +60cm
Label everything
Draw diagram in two different colors
Purple = straight from top of object to interface, goes from there through PPF on other side
Blue = top of object through APF to interface, then goes parallel on other side
From where blue and purple meet of other side of the interface to the optic axis is the image location
Accurate ray diagrams will show min or mag
Negative sign says image is upside down from object
Minified image M < 1
Inverted image = - M
OBJECT-IMAGE PATTERNS (HW “image location”)
1. Object at 2APF will give image at 2PPF, vergences will be the same strength but opposite signs,
object and image will be same size
2. Object at APF will give image (draw nodal ray) at infinity, inverted, image infinitely larger than
object
3. Object between 2APF and infinity gives image between PPF and 2PPF, image is minimized and
inverted, object vergence is weaker than image vergence
4. Object between APF and 2APF gives image b/w 2PPF and infinity, image larger and inverted
5. Object between APF and SRS gives virtual image anterior to refracting surface, image larger and
upright, on same side as object (real object and virtual image are both anterior to SRS)