Diffraction of light
Aim:
Find the slit width of single slit, bled slit and aperture width of double slit.
Apparatus:-
He Ne laser
Optical batch
Slits (single slit, double slit and bled slit)
Slit stand
White screen
Theory:-
Consider the light rays from the two coherent point sources made from infinitesimal slit 𝑎
distance d apart. We assume that the sources are emitting monochromatic light of wavelength λ.
The rays are emitted in all forward directions. But let us concentrate on only the rays that are
emitted in direction 𝜃 toward a distant screen (measured from the normal to the screen, diagram
below). One of these rays has further to travel to reach the screen and the path difference is given
by d sin 𝜃. If this path difference is exactly one wavelength λ or an integer number of wavelengths,
then the two waves arrive at the screen in phase and there is constructive interference, resulting in
a bright area on the screen. If the path difference is λ, or 𝜆, 𝑒𝑡𝑐. then there is destructive
interference, resulting in a dark area on the screen.
𝑏𝑟𝑖𝑔ℎ𝑡: 𝑑 sin 𝜃 = 𝑛𝜆
1 𝑛 = 0, ±1, ±2..
𝐷𝑎𝑟𝑙: 𝑑 sin 𝜃 = 𝑛 + 𝜆.
2
If 𝜃 is small, then sin 𝜃 ≅ 𝜃 (𝜃 𝑖𝑛 𝑟𝑎𝑑𝑠!) and maxima occur on the screen at 𝜃 = 𝑛 ; minima
occur at 𝜃 = 𝑛 + .
A complete analysis (not show here) yields a pattern of intensity vs. angle that looks like:
In fact, this regular-looking pattern is not observed in practice. Because real slits always
have finite width (not an infinitesimal, width). We now ask what is the intensity pattern from a
single slit of finite width a? Huygens’ Principle states that the light coming from an aperture is the
same of the aperture. To see what pattern the entire array produces, consider first just two of these
imaginary sources: one at the edge of the slit and one in the center. These two sources are separated
by a distance 𝑎⁄2.
The path difference for the rays from these two source, going to the screen at an angle𝜃,
Is sin 𝜃, and these rays will interfere destructively if sin 𝜃 = . But the same can be said for
every pair of sources separated by 𝑎⁄2. Consequently, the rays from all the sources filling the
aperture cancel in pairs, producing zero intensity on the screen when sin 𝜃 = or, if 𝜃 is small,
𝜃 = . (First minimum in single slit pattern.)
A complete analysis (too complicated to show here) yields an intensity pattern, called a diffraction
pattern, on the screen that looks like…
(The central maximum is actually much higher than shown here. It was reduced by a factor of 6,
for clarity.) The single slit diffraction pattern has minima at
𝜆 2𝜆 3𝜆
𝜃= ± ,± ,± , … . . (𝑚𝑖𝑛𝑖𝑚𝑎 𝑜𝑓 𝑠𝑖𝑛𝑔𝑙𝑒 𝑠𝑙𝑖𝑡 𝑝𝑎𝑡𝑡𝑒𝑟𝑛. )
𝑎 𝑎 𝑎
So the separation of minima is 𝜆⁄𝑎 , except for the first minima on either side of the central
maximum, which are separated by 2𝜆⁄𝑎.
When the aperture consists of two finite slits, each of width a separated by a distance d, the
intensity pattern exhibits a two-slit interference pattern modulated by a single slit diffraction
pattern:
In this full pattern, the finely spaced interference maxima are spaced ∆𝜃 = . while the more
widely spaced minima of the single-slit diffraction pattern are separated by ∆𝜃 = 𝑜𝑟 .
Note that an interference maximum can be wiped out if it coincides with a diffraction minimum.
Procedure:-
1. Mount the He-Ne laser on the rod provided with it by sliding the screw of the mounting rod
into the slot (at the bottom of laser) and the tighten it.
2. Mount the He-Ne laser with its mounting rod on the saddle of the optical bench. Position the
saddle at one end of the optical bench.
3. Mount the slide with blade on the slide holder.
4. Mount the screen (30 x 30 cm) on the cylindrical base and hold a graph paper on it using clip.
Place the screen at a distance of about 2-3m from the slide holder.
5. Shine the laser beam on the screen and carefully edge the blades into beam.
6. Adjust the height and position of the slit in front of the laser beam to obtain distinct maxima
and minima.
7. Measure the distance ‘x’ between the midpoint of central maximum and the midpoint of first
minimum obtained on the graph paper. Find ‘x’ on both sides of central maximum and take
mean of the two values.
8. Measure the distance between the slit and the screen using measuring tape.
9. Measure the slit width‘d’ using a travelling microscope.
10. Take few set of observations by changing the distance between the slit and the screen‘d’ and
slit width‘d’.
(Note: Slit width can be changed by carefully adjusting the screws using a screw driver.)
Observations:-
(a) For single slit:
Sr. 𝝀𝑫
𝝀 (nm) D (cm) 𝒙 (𝐜𝐦) 𝒅= Mean value of 𝒅 (𝒄𝒎)
no 𝒙
1 632.8 120
2 632.8 90
3 632.8 60
(b) For blade slit
Sr. 𝝀𝑫
𝝀 (nm) D (cm) 𝒙 (cm) 𝒅= Mean value of 𝒅 (𝒄𝒎)
no 𝒙
1 632.8 120
2 632.8 90
3 632.8 60
(c) For double slit
Sr. 𝝀𝑫
𝝀 (nm) D (cm) 𝒙 (cm) 𝒅= Mean value of 𝒅 (𝒄𝒎)
no 𝒙
1 632.8 120
2 632.8 90
3 632.8 60
Calculation:-
λ=
(Standard Value of λ = 632.8 nm)
Mean Width of slit
𝑑 +𝑑 +𝑑
𝑑=
3
Result:
Mean value of
1. Single slit is _________________cm
2. Blade slit is _______________cm.
3. Double slit is _______________𝑐𝑚.
Conclusion:
Date: Signature:
