by Din » Sat Oct 17, 2020 9:00 am
If you have two point sources, as in your diagram, then you will get a sinusoidal variation of light bands and dark bands. The defining equations is:
m*λ = d*sin(θ)
where m is called the 'order' of the pattern (the pattern repeats - dark, light, dark, light etc) ), d is the distance between two slits, λ is the wavelength and θ is the angle between any point on the screen and a normal (straight line) from half way between the slits. So, let us say that you set up your two slits (if you're using a laser, you don't need the first slit) separated by 0.02 mm and you measure the third bright point on your screen to be at an angle of 5.45 degrees from the centre of the slit system, what is the wavelength?
λ = d*sin(θ)/m = {(0.02)*sin(5.45)}/3 = 0.000633
The intensity variation is sinusoidal, and is given by
I(t) = 4*I* cos²(θ/2)
where I(t) is the total intensity at the screen, and I is the intensity at each slit. So, if you imagine a cos² curve, the fringe system follows the curve.
This is for a two slit system, as you've drawn. However, in holography, we usually have a planar (flat) wave and a diverging wave from a point source. In this case, the fringe system is hyperbolic, the lines of equal intensity are shaped like hyperbolas. Depending on where you place the film, the film will intersect the hyperbolas and form the fringe system. Below is a diagram from "Optical Holography" by Collier, Lin and Burckhardt
- fringes.jpg (206.78 KiB) Viewed 7692 times
If you have two point sources, as in your diagram, then you will get a sinusoidal variation of light bands and dark bands. The defining equations is:
m*λ = d*sin(θ)
where m is called the 'order' of the pattern (the pattern repeats - dark, light, dark, light etc) ), d is the distance between two slits, λ is the wavelength and θ is the angle between any point on the screen and a normal (straight line) from half way between the slits. So, let us say that you set up your two slits (if you're using a laser, you don't need the first slit) separated by 0.02 mm and you measure the third bright point on your screen to be at an angle of 5.45 degrees from the centre of the slit system, what is the wavelength?
λ = d*sin(θ)/m = {(0.02)*sin(5.45)}/3 = 0.000633
The intensity variation is sinusoidal, and is given by
I(t) = 4*I* cos²(θ/2)
where I(t) is the total intensity at the screen, and I is the intensity at each slit. So, if you imagine a cos² curve, the fringe system follows the curve.
This is for a two slit system, as you've drawn. However, in holography, we usually have a planar (flat) wave and a diverging wave from a point source. In this case, the fringe system is hyperbolic, the lines of equal intensity are shaped like hyperbolas. Depending on where you place the film, the film will intersect the hyperbolas and form the fringe system. Below is a diagram from "Optical Holography" by Collier, Lin and Burckhardt
[attachment=0]fringes.jpg[/attachment]