Wave Optics
- light acts like a particle
- Einstein proved this with his photoelectric effect
- light acts like a wave
- Thomas Young proved this with the double slit
Light has properties of both waves and particles
Conditions for Interference
1. Two or more interfering waves travel through different regions of space
2. Waves are brought together at a common point
3. Light waves must have the same frequency and a fixed relationship
Young’s Double Slit Experiment
Double Slit Interference Pattern from three different lasers
Bright areas – constructive interference (bright fringe)
Dark areas – destructive interference (dark fringe)
Constructive interference occurs when ΔL = nλ
ΔL also equals dsinϴ
d sinϴ = nλ constructive
d sinϴ = (n+ ½) λ destructive
d= distance between the slits
AP uses m instead of n – they both represent the order of the
maximum or minimum
Often you are asked to find a
distance on the screen.
Use tanϴ =
The AP formula sheet uses x
instead of y and does small angle
approximation. (tanθ = sinθ)
Their formula is
Xm ≈ λ

Young’s Double Slit experiment
Example 1 –
Red light (λ = 664 nm in a vacuum) is used in Young’s experiment with the slit separated by a
distance d = 1.20 X 10-4 m. The screen is located at a distance of 2.75 m from the slits. Find the
distance on the screen between the central bright and the third order fringe.
Single Slits and Diffraction Gratings
A diffraction grating consists of a large # of slits
-the locations of the bright and dark spots is exactly the same as it is
for a double slit
-use the same formulas as a double slit
Single Slit
-only need to know the pattern for the single slit
Single Slit has a wider and more intense central maximum – other maximums are
evenly spaced but narrower and not as intense
Double Slit all the maximums and minimums are the same width but vary in intensity
– the central maximum being the most intense
Intensity Patterns for Single and Double Slits
Single Slit
-wider central max
-more intense (brighter)
Double Slit
- Central max same size as
other maximums
- Central max more intense
Diagram below shows a thin film of gasoline floating on water
- at the top surface of the film reflection occurs (Ray 1)
- refraction also occurs – enters the film and is reflected from the
bottom layer (Ray 2)
Ray 2 has traveled farther than ray 1
The difference in path lengths occurs in
the film
Therefore the wavelength that is
important for thin lens interference is the
wavelength in the film
Phase Changes for Light
1. When light travels from a lower to a higher index of refraction
(air to water) reflection occurs at the boundary along with a
phase change equal to ½ a wavelength
2. When light travels from a higher to a lower index of refraction
(gasoline to water) there is no phase change upon reflection
Extra distance traveled = 2t
Constructive interference = mλ (m=1,2,3,…)
- air to gasoline ½ λ phase change
- gasoline to water no phase change
2t + ½ λ = mλ
Destructive interference = (m + ½ )λ (m=1,2,3,..)
2t + ½ λ = (m + ½ )λ

Conditions for Interference