Check out the Original Double Slit Experiment

https://www.youtube.com/watch?v=Iuv6hY6zsd0

## Pre-lecture Study Resources

Watch the pre-lecture videos and read through the OpenStax text before doing the pre-lecture homework or attending class.

### BoxSand Videos

## Required Videos

Young's Double Slit - Apparatus and conceptual (15min)

## Suggested Supplemental Videos

### Learning Objectives

## Summary

Summary

## Atomistic Goals

Students will be able to...

### BoxSand Introduction

## Wave Optics | Young's Double Slit Experiment

**Superposition of Waves**

When two waves enter the same region of space at the same time they interfere in a way that obeys the Superposition of Waves. This addition of waves creates places where the peaks line up and the resultant wave is larger, which would manifest as a bright spot for light waves. There are also regions where the peak from one wave is lined up with the trough from the other and the resultant is wave cancelation, where their amplitudes add to zero and there would be a dark spot. These constructive and destructive areas are seperated by an entire gradient of partially constructive and partially destructive. The resulting interference pattern is one of the defining features of a wave.

**Wave Interpretation of Light - Young's Double Slit Interference**

The theory of Electromagnetic Radiation Wave Theory is one of the most tested and confirmed theories in physics. It relies heavily on the experimental fact that light has wave-like properties. These wave-like properties are displayed by the interference effects that has only been observed in wave systems. The hallmark experiment that enabled us to observe the effect was Young's Double Slit Experiement.

To observe the interference of two sources you need two, coherent, single frequency sources. Essentially you would like two identical sources. The clever way Young achieved this was by isolating a single color of light then sending that light through two small slits. Each slit acts like a new wave source due to the diffraction of light, which is the effect that light "bends" around corners and spreads out when passing through an opening. Since each slit acts like a new source, and each originated from the same source, they are two coherent, single frequency (same color) sources. The diagram below shows a snapshot of the waves as they interfere.

The modern technology of a LASER (Light Amplification through the Stimulation of Electromagnetic Radiation) has made this experiment much easier due to the very high intensity soures they provide. The experiment also enables one to measure the wavelength of visable light, something on the order of hundreds of nanometers, a size only an order of magnitude greater than the size of atoms. For nearly 100 years this was the only way to probe scales this size scale and it still remains as one of the best.

The geometry of Young's Double Slit is below.

Here the dstance between the slits is $d* $* and the screen observing the interference effect is a distance $D$ away from the slits. The central maximum is located along the perpendicular bisector between the two sources where the

*(*

**Path Length Difference***PLD*) between the two sources is zero. The condition for constructive interference is for the

*PLD*to be an interger ($m$) multiple of the wavelength. So as you move away from the central maximum and go from constructive to destructive and back to constructive, you've increased the

*by one whole wavelength. These bright spots are called*

**PLD***interference fringes*. Using the condition for constructive interference $PLD = m \lambda$ and the geometery that $PLD=d sin(\theta)$, you arrive at the overall condition for constructive interference.

$d sin{\theta}=m \lambda$

The distance $y$ is measured from the central maximum and can be related to the angle ($\theta$) and the distance $D$ by the equation $tan (\theta) = \frac{y}{D}$. In most cases, where $\lambda << d$ the angle is so small that $sin (\theta) \approx \theta$. Since $tan (\theta) = \frac{sin(\theta)}{\cos(\theta)}$ and $\cos(\theta) \approx 1$ for very small angles, $tan(\theta) \approx sin(\theta) \approx \theta$. This allows a more simple connection between the variables shown in the equation below, but note, this only if the angles are very small.

$y \approx \frac{m \lambda D}{d}$, if $\lambda << d$

## Key Equations and Infographics

Now, take a look at the pre-lecture reading and videos below.

### OpenStax Reading

OpenStax Section 27.2 | Huygens's Principle: Diffraction

OpenStax Section 27.3 | Young's Double Slit Experiment

## Additional Study Resources

Use the supplemental resources below to support your post-lecture study.

### YouTube Videos

Here is another good introduction to the Double Slit Experiment

https://www.youtube.com/watch?v=uva6gBEpfDY

Some mathematics behind double slit diffraction,

### Simulations

Phet - wave interference,

For additional simulations on this subject, visit the simulations repository.

### Demos

Lake Experiment #2 - Wave Interference(1min)

Lake Experiment #2 - Wave Interference(1min)

For additional demos involving this subject, visit the demo repository

### History

Oh no, we haven't been able to write up a history overview for this topic. If you'd like to contribute, contact the director of BoxSand, KC Walsh (walshke@oregonstate.edu).

### Physics Fun

Check out Dr. Quantum explore the double slit experiment from a quantum physics perspective.

### Other Resources

## Problem Solving Guide

Use the Tips and Tricks below to support your post-lecture study.

### Assumptions

### Checklist

1. Read the problem carefully and visualize the physical setup.

2. Determine if it is indeed a problem best analyzed with wave optics and not ray optics.

3. Determine what physical model best fits the problem. Is it a double, multi, or single slit interference or is a thin film effect?

4. For the type of system, draw the appropriate physical representation.

5. Organize the relevant equations for the specific system.

6. Determine what variables are known or unknown. Perhaps what variables are changing - is it a proportional reasoning problem?

7. If it is a slit problem, is it in the small angle approximation? If so, how does this simplify the equations?

8. Solve the system of equations, perhaps with the use of geometry (this is a big step and mastery comes with practice).

9. Check your answer for reasonableness. Magnitude, dimensions, limiting cases?

### Misconceptions & Mistakes

- ... students mistakenly assume all the interference patterns are the same
- ... students mistakenly make the small angle approximation for all cases
- ... students mistakenly ignore the $\pi$ phase shifts in certain reflections in a thin film interference

### Pro Tips

- Draw the physical representation - being able to see the fringes and the geometry is very useful

### Multiple Representations

Multiple Representations is the concept that a physical phenomena can be expressed in different ways.

### Physical

The diagram for Young's double slit experiment depicts the important features used to describe the phenomena.

From a single slit diffraction to mutli slit diffraction the single slit forms an envelope where the sharpness of bright peaks become more sharp as the number of slits is increased.

### Mathematical

### Graphical

### Descriptive

### Experimental

Check out this easy to do at home experiment to observe Young's double slit experiment.

## Practice

Use the practice problem sets below to strengthen your knowledge of this topic.

### Fundamental examples

(1) A red laser with wavelength $\lambda = 700$ nm shined on a double-slit with width $d=10$ mm. The screen is located $D= 2 $ m away from the slit. How far up from the central maximum is the $m=2$ bright fringe?

(2) How does the position of the 2nd bright fringe in example 1 change if the wavelength used is $\lambda_{new} = 350$ nm instead of $\lambda_{old} = 700 $ nm?

(3) In a single-slit experiment, the width of the central maximum is $1.5 $ mm. The screen is 1 meter from the slit and the wavelength of light used in this experiment is $360 $ nm. (a) What is the size of the slit? (b) How much wider would the central maximum be if the wavelength was tripled?

(4) In a single-slit experiment, the second dark fringe is located 7.5 cm from the center of the central maximum on a screen located $L = 3 m$ away from the slit. What is the distance between the second dark fringe and the third dark fringe that is located *on the other side of the central maximum*? The wavelength of the illuminating light is $\lambda = 600 $ nm.

Solutions found HERE

Short foundation building questions, often used as clicker questions, can be found in the clicker questions repository for this subject.

### Practice Problems

Conceptual Problems

BoxSand's multiple select problems

BoxSand's quantitative problems

Recommended example practice problems

- PhysLabs
- Double Slit Worksheet: Website Link
- Single Slit Worksheet: Website Link

- OpenStax Practice problems at the end of sections
- Young's Double Slit: Website Link
- Multiple Slit Diffraction: Website Link
- Single Slit Diffraction: Website Link

For additional practice problems and worked examples, visit the link below. If you've found example problems that you've used please help us out and submit them to the student contributed content section.