Example

Two identical point sources produce water waves with a wavelength of 0.04 m. The sources are 0.1 m apart. What is the maximum angle for a line of total constructive interference and what is the value of n for this line?

Plane water waves

If you have a line of point sources, it is called a line source.

This produces wavecrests that are straight and parallel to the line source.

These are called plane waves.

Plane water waves hit a barrier with holes

Plane waves hit a barrier that has two openings, or “slits” in it.

The waves eminating from each slit look like those from a point source.

A slit thus acts as a point source when plane waves hit the barrier.

What is light?

Isaac Newton believed that light was made of particles that he called corpuscles.

Young’s double slit experiment for light showed an interference pattern that looked like those of water waves.

So light is a WAVE!

Young’s Double Slit Experiment

Bright fringes are maxima (total constructive interference) and dark fringes are minima (total destructive interference).

n=0 is the central maximum;

n=1 is the first fringe, etc.

Measure wavelength of different colors of light

Red light spreads out more than blue light.

Diffraction

When light passes through a slit, it bends around the slit. This effect is called diffraction.

A device with many slits is called a diffraction grating. Each slit acts as a point source. Total constructive and total destructive interference result in bright fringes (maxima) and dark fringes (minima).

The angles of the maxima are given by

Spread in maxima depends on wavelength

Red spreads more than blue

Blue spreads less than red

White light

Because the angle (i.e. spread) of bright fringes depends on wavelength, a diffraction grating will separate white light into its spectrum.

Wavelengths of Colors

Region Wavelength (nm)Violet 440 nm - 400 nmBlue 480 nm - 440 nmGreen 560 nm - 480 nmYellow 590 nm - 560 nmOrange 630 nm - 590 nmRed 700 nm - 630 nm

Poll

If the distance between slits of a diffraction grating is increased, what will happen to the distance between the central maximum and first bright fringe?

1. it will increase (more spread out)

2. it will decrease (less spread out)

3. it will remain the same

Poll

Which color has a fringe further from the central maximum, red or blue?

1. red

2. blue

3. neither, because their fringes will be at the same location relative to the central maximum

Speed of Light

Light has a finite speed. According to NIST, the meter was defined to be the length of a certain platinum bar kept at constant temperature in Paris. Using this standard, the speed of light in a vacuum was measured to be

Rather than continuing to try to measure the speed of light more precisely, based on the length of a stick in Paris, instead the speed of light was defined as this value, and the meter was redefined to be the distance light travels in 1/299,792,458 s.

Speed of light in a medium

When light travels through a medium, such as glass for example, then it travels slowe than in a vacuum. As a result, it will have a shorter wavelength. Its wavelength in a medium is related to its wavelength in vacuum by

Other types of interference

Phase change upon reflection

Suppose that light travels from vacuum to glass. It both reflects and transmits at the vacuum/glass surface. The reflected wave will have a phase shift of 180 which corresponds to half a wavelength.

If light travels from a slower medium to a faster medium, it does not change phase (in other words, is not shifted by half a wavelength)

Interference from multiple reflections

thickness, d

for total constructive interference