Young’s Experiment
Introduction & Theory
Diffraction patterns of bright and dark fringes occur when monochromatic light passes through a single or
double slit. Fringe patterns also result when light passes through more than two slits. The arrangement
consisting of a large number of parallel, closely spaced slits is called a diffraction grating. When Thomas
Young performed his historic experiment, he passed monochromatic light through a single slit and
obtained an interference pattern as shown below. Notice that most of the light intensity is concentrated in
the broad central diffraction maximum.
He found an inverse relationship between the width of the slit and the width of the diffraction pattern; the
wider the slot, the narrower and sharper the central peak.
When two slits are used, the intensities of the fringes produced are modified by the diffraction of the light
passing through each slit as shown below (a).
(a)
The intensity plot obtained with one slit acts like an envelope, limiting the intensity of the double slit
fringes. Notice that the first minima of the single slit pattern of (b) below, eliminates the double-slit
fringes that would occur near the 12° mark (c) below.
When there are more than two slits used, the intensity pattern far away is a combination of the single-slit
pattern of the individual slits and the two slit pattern just discussed. Assuming that the slit width is small
compared to the wavelength of the incident light, constructive interference patterns occur as shown below.
As the number of slits increases, the bright fringes become larger and narrower, with more intervening
minima. In the experiment presented here, we will use a neon laser for the monochromatic source, and a
diffraction grating to produce a multi-slit diffraction pattern, as shown below.
The distance between the slits is given as d, and ym is the distance between the oth or central intensity
maximum (m = 0) and the nth intensity maximum (m=±1,± 2, ±3, etc). The angle θn is formed between
the centerline and the nth maximum, and is given by the relationship:
sin θ n =
mλ
d
where m = ±1, ±2, ±3, …
(1)
and λ is the wavelength of the monochromatic light. This is Young’s Equation.
The distance between the diffraction grating and the target screen is the length L, defined in the geometric
relationship:
tan θ n =
yn
L
(2)
Objectives
The objectives of this experiment are:
1. Emulate Young’s experiment, solving Young’s equation for the angular displacement to the first
maximum intensity peak, using equation (1), and a known diffraction grating.
2. Verify the angular displacement to the fist intensity maximum by experimentally measuring the
target distance (L), and the distance between the central intensity maximum and the first intensity
maximum, and solving equation (2).
3. Calculate the experimental error between the calculated and measured angular displacement.
Equipment
Neon Laser, λ = 650 nm
Pasco Diffraction Grating, 600 lines / mm
Meter stick
Pasco Optics Bench, Ray Table Base
Magnetic Component Holder Plate (2)
Target Plate (Viewing Screen)
Procedure
1. Place the neon laser on one end of the optics table base and line up the laser, diffraction grating,
and the target, using the magnetic slit plates as shown below.
2. Calculate the distance between slits as the reciprocal of the # lines/ mm:
1
d=
= 1.667 × 10 −6 m
600lines / mm
3. Operate the laser, being careful to follow all safety precautions.
4. Place the diffraction grating close to the laser aperture and place the display screen at a convenient
distance away from the diffraction grating to arrange to measure the distances between the
maximum intensity lines.
5. Using Young’s equation, calculate the angular displacement θ1 from the central intensity
6.
7.
8.
9.
⎛λ⎞
maximum to the first intensity maximum as: θ1 = sin −1 ⎜ ⎟
⎝d ⎠
Measure the distance between the diffraction grating and the target screen (L), and the distance
between the central intensity maximum and the first intensity maximum (y1).
⎛y ⎞
Determine θ1 using the measured geometric data and the relationship: θ 1 = tan −1 ⎜ 1 ⎟
⎝L⎠
Compare the angles determined in steps 5 & 7 and calculate the percent error as:
⎛ θ − θ meas ⎞
⎟⎟ × 100%
%error = ⎜⎜ calc
θ calc
⎝
⎠
Repeat steps 5-8 using the m = -1 and the m = ± 2 intensity maxima as time permits
Conclusion
1. Comment of the validity of this experiment with respect to Young’s historic single and double slit
experiments.
2. Write a statement comparing the measured and computed values of θm with possible sources of
error, and suggestions for improving the accuracy of the experiment.