For water waves, this can be done by two sources. For light, there is an extra problem: sources don't stay in phase...
Huyghen's Principle
Every point on a wave acts as a source of new (spherical) wavelets
When these add together (interfere constructively) one gets a new wavefront
Huyghen's principle allows us to understand a variety of phenomena: e.g refraction.
We can use this to understand how waves pass through narrow gaps
Each successive wave is "in phase with itself"
Can replace two sources by one source and two slits: Young's slits experiment
e.g. a light produces Na light (λ = 589 nm) and it passes through two slits separated by 50μ (5x10-5 m). How will it appear on a screen at a distance of 1 m?
What is the distance from the central max to the 2nd max?
We can go from one slit to "many": this gives us a diffraction grating
Waves can go straight through. Wow! However, this isn't very interesting!
What makes diffraction gratings interesting is that bands are very narrow:
even if one slit and the next produce waves that are only 10 out of phase, the 180th slit will be completely out of phase, so they only add up at one angle.
Geometry:
λ = d sin(θ)
so if white light is incident on diff. grating, it will be split up into constituent wavelengths
We may also be able to arrange a second maximum
2λ = d sin(θ₂)
e.g. Na light consists of two wavelengths very close to 589 nm. It is incident on a diffraction grating with 8000 lines/cm. What will you see?
At what angle will the first maximum be found?
Note that a diffraction grating is really an interference grating...)
Single Slit
Can also get interference effects with a single slit
Geometry
To have destructive interference between light from centre and edges, need
e.g. Na light falls on a slit .1 mm wide: at what angle is the first max?
Actually, there are additional complications here:
The intensity falls of very rapidly away from the centre line.
Minima are given by
sin(θ) = mλ m = 1,2,3.. (but not m=0)
a
Centre (bright) is given by m=0
Maxima are given by
sin(θ) = (m+½)λ m = 1,2,3.. (but not m=0)
a
Thin Film interference
Can get reflections from two different surfaces, and depending on path difference these can interfere
e.g. a wedge:
if the light from the bottom level travels λ/2 further, there will be destructive interference between the two reflections. Since the path will depend on the separation, there will be a pattern of lines
e.g. suppose we are using hydrogen light (λ = 643 nm) and the wedge has an angle of .001 radians, what will the separation between the lines be?
d₂-d₁ = λ
We can use this constructively to reduce the reflection from lenses: e.g. a surface will reflect
By coating the lens, we can arrange for destructive interference in the reflected wave
Dispersion
Glass has (slightly) different refractive indices n for different λ, Hence a prism can be used to produce a spectrum.
Note that this mechanism is quite different from a diffraction grating (where different wavelengths interfere constructively at different angles).
With a prism, the red light is deviated least (i.e. the velocity is largest), whereas for a grating it is deviated most.
Refraction shows up in the atmosphere: e.g.
Mirages: Hot air is less dense than cold air
Green Flash
Atmosphere bends light, but blue is bent most. Hence image of the "blue" sun is sometimes visible just after sunset, or just before sunrise. You see this as a momentary "green flash" lasting for about 2 s. Need a distant horizon (i.e. mountains or sea) to give an adequate distance through the atmosphere
Rainbows:
combination of refraction and total internal reflection in raindrop.
Given this explanation of the rainbow, which colour would be on the outside of the arc?
red
blue
green
yellow
.
Why is the sky darker outside the rainbow than inside?
Now we understand physical optics and geometric optics, we can look at how optical instruments work
.