Interference Patterns

This report will be performed by a group of 3 students viz. Harleen Kaur, Rutvi Patel and Sandhya, determining the wavelength of light from a laser using a double – slit slide. The laser was shone through the double – slit such that it projected interference pattern onto the paper screen. The experiment will be repeated three times varying the distance between the slit and the screen to understand the effective relationships. The expected wavelength of the laser light is 6.5 X 10-7, however, the value found of the wavelength is 7.56 X 10-7 with an error of 16.3%. The difference in values is due to human and random errors. YOUNG’S DOUBLE SLIT EXPERIMENT

Interference Patterns

This report will be performed by a group of 3 students viz. Harleen Kaur, Rutvi Patel and Sandhya, determining the wavelength of light from a laser using a double – slit slide. The laser was shone through the double – slit such that it projected interference pattern onto the paper screen. The experiment will be repeated three times varying the distance between the slit and the screen to understand the effective relationships. The expected wavelength of the laser light is 6.5 X 10-7, however, the value found of the wavelength is 7.56 X 10-7 with an error of 16.3%. The difference in values is due to human and random errors.

Ms. KATHERINE KEEHarleen Kaur

12-05-15

Harleen Kaur

12-05-15

INTRODUCTION

An English scientist, Thomas Young, first performed the double slit experiment in the early 1800s. In this experiment, light was allowed to diffract through slits, which produced fringes, or wave-like interference patterns on an opposing screen. In the basic version of the experiment, a coherent light source, e.g. laser beam, illuminates a thin double slit plate, and the light passing through the slits is observed on a screen behind the plate. The wave nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen — a result that would not be expected if light consisted strictly of particles. As a modern version of this experiment, the quantum double slit experiments are performed using photons, electrons, neutrons and others. It is necessary to use quantum mechanics in order to explain the interference pattern for sub- atomic particles. THEORY

In a double slit experiment, a single light source is split into two, thus generating two coherent sources. When the light from the two coherent sources is projected on the screen, interference pattern is observed as illustrated in the figure below:

In the figure above, light bands are observed at the regions of constructive interference {resultant of two superposed waves that are in-phase) while dark bands are observed at the regions of destructive interference {resultant of two superposed waves that are at a phase difference of λ2}.

In the figure below, two light rays pass through two slits, separated by a distance d and strike a screen a distance, L , from the slits: X

X

S1

S1

S2

S2

S2X – S1X = λ2

∴ S2X – S1X = n- 12 λ

* As it is difficult to measure θ, it is best to find a valuation for sin θ in terms of dimensions, that can be measured. λ2d=sinθ

∴ λ2=dsinθ

∴ sinθ=n- 12λd

where n = 1, 2, 3, … {order from center line}

* As L gets very big compared to y, the distances S1X and S2X become more parallel. * As angles get very small;

sinθ ~tanθ ~ xL

xnL=n- 12 λd

∴ ∆xL= λd

HYPOTHESIS

The wavelength of the laser light that is to be determined should be same of close enough { due to experimental and random errors} to the given value of the laser. The wavelength of the light source can be found by the equation: ∴ ∆xL= λd

where ∆x is distance between two dark bands

L is the distance between slit and screen

d is the distance between the two slits

EXPERIMENTAL DESIGN

MATERIALS REQUIRED:

* 1 red laser

* 1 double slit slide {d =...