Experiment 12: Double-Slit Interference Pattern Theory For a double-slit system, the angular location of the maxima of the interference pattern (bright fringes) on the viewing screen is given by: dsinθm=mλ  (m=  0, 1, 2, 3,

Experiment 12: Double-Slit Interference Pattern

Theory

For a double-slit system, the angular location of the maxima of the interference pattern (bright fringes) on the viewing screen is given by:

dsinθm=mλ  (m=  0, 1, 2, 3, ...) 

whereas the angular location of the minima (dark fringes) is given by

dsinθn=n+12λ  (n=  0, 1, 2, 3, ...) 

In these formulas,  d

 is the distance between the slits (slit spacing), θm(n)

 is an angle between direction to the respective maximum (or minimum) and the main optical axis of the system, and λ

 is the wavelength of the incoming light. Integer number m

 (n

) is called the order of the fringe.

If λ?d

, the low order bright fringes on the viewing screen at distance D

 from the double-slit screen are equidistant and separated by the distance

?x≈λDd

In this lab, we’ll observe interference pattern in the Young’s double-slit experiment and explore how this pattern depends on the wavelength of the incoming light λ

, slit spacing d

, and the distance between the screens D

.

Procedure

Physics Simulations: Double Slit Interference

https://www.geogebra.org/m/ZSbeWGbe

Experiment

Set the width of the slit a=1μm

. We will not change the width of the slit in this experiment.

The values of λ, d

 and D

 can be changed by moving the dots in the experiment window. The interference pattern on the viewing screen is displayed in the experiment window if you check “Show Both” box (Do not check other boxes to see the clear pattern!).

1. Gradually change the wavelength of light λ

   

    while keeping the slit spacing d

   

    and the distance between the screens D

   

    constant. Describe and explain using theoretical formulas how the distance between the bright fringes ?x

   

    depends on λ

   

2. Gradually change the slit spacing d

   

    while keeping the wavelength of light λ

   

    and the distance between the screens D

   

    constant. Describe and explain using theoretical formulas how the distance between the bright fringes ?x

   

    depends on d

   

   .

3. Gradually change the distance between the screens D

   

    while keeping the wavelength of light λ

   

    and the slit spacing d

   

    constant. Describe and explain using theoretical formulas how the distance between the bright fringes ?x

   

    depends on D

   

   .

Questions:

1. Light of what color yields the maximum separation of the fringes?

2. If you increase the slit spacing how should you change the distance between the screens in order to keep fringes in the same positions?