Lecture 37

Readings

Experiments that show the wave nature of light :
- Single Slit :
  - Ray Model :
  - Actual :
  - Double Slit :
Waves exist in 2-D and 3-D , "ripples in a pond"
Energy gets "spread out" in 2-D and 3-D cases - ripples die down with distance
2 Slit Explanation
- Each slit is a "point source" of an expanding wave - the crests going out
- When crest from top slit coincides ( at some location ) with crest from other slit , you will get the maximum signal ( constructive interference )
- When crest from 1 slit coincides with valley from other , you will get zero signal ( destructive interference )
Math of Constructive and Destructive Interference :

Δ ϕ = \frac{2 * π * Δ r}{λ}

Δ r = | r_{1} - r_{2} |

$r_1$ is the distance from slit 1 to the point of interest
- A point on the screen
$r_2$ is distance from slit 2 to a point on the screen
$\Delta \phi$ $\pi$ $(0 , 2\pi , 4\pi , etc)$ , then constructive interference occurs
- This is the same thing as saying that :
  - $\Delta r$ $\lambda : \Delta r = 0 ,\lambda , 2\lambda , etc$
$\Delta \phi$ $\pi$ $(1\pi , 3\pi , 5\pi , etc)$ , then destructive interference occurs
- This is the same thing as saying that :
  - $\Delta r$ $\lambda : 0.5\lambda , 1.5\lambda , 2.5\lambda , etc$