1. Phy2005 Applied Physics II Spring 2017 Announcements:
Exam III April 10 in-class
Anne Tolson review Thurs/Fri 5pm?
Review Sunday, April 9 4pm NPB 2205 (upstairs)
Coverage: Chs NOT

2. Exactly the same as the mirror eq.!!! Now let’s think about the sign.
Last time
Lens equation and magnification
1/p + 1/q = 1/f
M = -q/p
Exactly the same as the mirror eq.!!!
Now let’s think about the sign.
positive
negative p
real object
virtual object
(multiple lenses) q
real image
(opposite side of object)
virtual image
(same side of object) f
for converging lens
for diverging lens M
erect image
inverted image

3. Last time
Nearsighted
Farsighted A

4. (two converging lenses)
Last time
Compound Microscope
(two converging lenses)
objective
eyepiece po qo pe
Magnified inverted virtual image qe
Real image formed by the objective lens  an object for the eyepiece lens

5. Interference and Diffraction of Light Wave
Christiaan Huygens
( )
Thomas Young
( )
His double slit experiment proved wave-like
nature of light.

6. Interference and Coherent Light Source
Any situation in which two or more waves overlap in space
Principle of Superposition
slinky

7. Whenever two portions of the same light arrive at the eye
by different routes, either exactly or very nearly in the
same direction, the light becomes most when the difference of the routes is any multiple of a certain length, and the least intense in the intermediate state of interfering portions; and this length is different for light of different colour.
T. Young from a paper to the Royal Society in 1802

8. Let’s compare interference of light and water waves
Veritasium
Laser double slit

9. |r1 – r2| = 0, l, 2l, 3l, …, ml (m: integer)  Constructive Int.
• P r1 r2
|r1 – r2| = 0, l, 2l, 3l, …, ml (m: integer)  Constructive Int.
|r1 – r2| = l/2, 3l/2, 5l/2, …, (2m+1)l/2  Destructive Int. l

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11. Q1. Two loudspeakers send out identical sound waves along
the x axis. The wavelength of the waves is 70 cm. One
speaker is at x=0. A listener is far away. The other
speaker starts at x=0 and moved along the x axis to the right.
At what 2nd speaker positions between 0<x<2m will the listener
hear the loudest sound? (assume both in phase) x
0.35m, 1.05m, 1.75m
0.0m, 0.5m,1.0m,1.5m,2.0m
only at 0.0m
(4) 0.0m, 0.7m; 1.4m
(5) only at 2.0m

12. |r1 - r2| = dsinq = ml Constructive Int.
● P q s1 s2 d
dsinq
Along the center line, it is obvious that the distances to
two sources are identical.  |r1-r2| = 0 and constructive int.
|r1 - r2| = dsinq = ml Constructive Int.
= (2m + 1)l/2 Destructive Int.
Approximation valid when d << r!!

13. ml (0, ±l, ±2l, …) Constructive dsinq =
(m+1)l/2 (±l/2, ±3l/2,…) Destructive
d(x/h) = ml  x = (h/d)ml for constructive int. d h q x 3 2
2nd-order bright fringe 1
1st order bright fringe

14. d = 0.05 cm h = 100 cm x = 0.36 cm d (x/h) = ml l = (d/m)(x/h)
Ex.28.1 In a certain double slit experiment, the slit separation is
0.050 cm. The slit-to-screen distance is 100 cm. When blue light
is used, the distance from the central fringe to the fourth-order
bright fringe is 0.36 cm. Find the wavelength of the blue light.
d = 0.05 cm
h = 100 cm
x = 0.36 cm
m = 4 constructive
d (x/h) = ml
l = (d/m)(x/h)
= (0.05/4)(0.36/100)
= 4.5 x 10-5 cm
= 450 nm

15. Note: this analysis is based on the assumptions that
the two light sources have exactly the same frequency
and they are absolutely in phase all the time.
Two identical monochromatic light source:
Same frequency and constant phase relation (could be in-phase)
Coherent Light Source

16. Huygen’s principle: Each point on a wavefront acts as a new
Coherent light sources by splitting
0th
2nd
1st
3rd
Huygen’s principle: Each point on a wavefront acts as a new
Source of identical waves.

17. You can tell when one light beam is a little behind
the other, because the pattern shifts! P
such a device is an “interferometer”

18. Interference in thin films
Ds =
Difference in two routes +
= 2x
(when qi << 1)
Half –reflecting planes
2x = ml constructive
= (2m+1)l/2 destructive x x q
For an arbitrary angle q
Ds = 2x/cosq