Question

1: A) Starting with two slits, separated by a distance "d," derive the key relation(s) associated with locating interference patterns.

B) Explain the effect on interference patterns if the number of slits is increased (but "d" remains the same).

C) Outline an experiment you can perform to determine the wavelength of a laser pointer (max intensity of 5mWatt) using "basic" lab equipment.

Answer 1

A). Youg's Double Slit experiment:-

This is a classic example of interference effects in light waves. Two light rays pass through two slits, separated by a distance d and strike a screen a distance, L , from the slits, as in Figure below.

If d < < L then the difference in path length r₁ - r₂ travelled by the two rays is approximately:

r₁ - r₂

Where angle '' is approximately equal to the angle that the rays make relative to a perpendicular line joining the slits to the screen.
If the rays were in phase when they passed through the slits, then the condition for constructive interference at the screen is:   

whereas the condition for destructive interference at the screen is:

The points of constructive interference will appear as bright bands on the screen and the points of destructive interference will appear as dark bands. These dark and bright spots are called interference fringes.

(i). In the case that y , the distance from the interference fringe to the point of the screen opposite the center of the slits is much less than L ( y < < L ), one can use the approximate formula:

  

  so that the formulas specifying the y - coordinates of the bright and dark spots, respectively are:

Brightspot

And Darkspot

The spacing between the darkspots is :

Note.: The above formulas assume that the slit width is very small compared to the wavelength of light, so that the slits behave essentially like point sources of light.

(B).We will get narrower peaks by increasing the no of slits. Let us Consider there is a huge amount of slits.Then, the waves travelling through each slit will all have different phases, and these phases will be equally distributed (if the slits are equally spaced). However, when you sum a huge number of sinus whose phases are equally distributed, we get something almost null: thus, the more slits there are, the nuller the diffraction figure will be. Nevertheless, at null incidence, there is no phase difference between each slit, so the are constructive interferences, and we see an intensity peak. Why is this maximum intenser as the number of slits increase ? We can understand this using energy conservation. There is always the same amount of energy that comes through the slits, but as the number of slits increases, it is more and more focused, so the maximum intensity increases as well.

(C). We can perform an experiment to detrermine the wavelength of LASER by Michelson Interferometer.Interferometers are used to precisely measure the wavelength of optical beams through the creation of interference patterns . The Michelson interferometer is a historically important device which provides simple interferometric configuration, useful for introducing basic principles.