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# 9.2. Single Slit Interference

Back in Section 4.4 we looked at Young's Double Slit experiment - a foundational experiment that demonstrates the wavelike nature of light through the phenomenon of wave interference. Light waves emanating from one slit interfere with light from the other slit, creating the characteristic interference pattern due to the path difference between sources. Interestingly, when we perform the same experiment with a single slit - we are also able to observe some wave interference. Veritasium made a nice little video which frames this section nicely, take a look.

We will explore the reasons behind why a single slit is also able to create its own characteristic interference pattern. The section has been divided up as follows:

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Single Slit Diffraction

#### Single Slit Diffraction

Brush up on the Young's Double Slit experiment from Section 4.4 and remind yourself about some of the key ideas and bits of vocab. Remember that it is the path difference between one slit and the other that causes an interference pattern to occur (either constructive if they the path difference is an integer multiple of λ, or destructive interference if the path difference is a half integer multiple of λ). Here we will observe that we can obtain an interference pattern with just a single slit.

If we go back to the Falstad ripple tank simulation we can observe the single slit interference pattern forming.

From the drop down menu, select the Single Slit option and observe the interference pattern.

## Single Slit Characteristics

If we use a viewing screen then we can see the single slit interference pattern. Notice that the x-axis in this case measures the angle in radians from the central line.

Our single slit interference pattern has the following key characteristics:

• A bright central maximum (approximately 20x as bright as the neighbouring maxima.

• Central maximum has double the angular width of the other maxima.

So why exactly do we observe an interference pattern with just one slit? This simulation by Geogebra shows that we have a path difference between the top of the slit and the bottom of the slit. Just like with the double slit, it is this path difference that causes our maxima and minima (bright and dark bits).

## Single Slit Equation

The single slit uses θ to measure the angle from the centre line. The single slit equation is presented below. One important difference is that our angle, θ, is the angle to the first minimum (whereas in our double slit equation we measure to the first bright fringe). You can find details of the full derivation here.

This Geogebra simulation allows you to change the slit width and wavelength to look at the resulting interference pattern. You will notice that the number of maxima changes depending on these slider values.

## Video Lessons

 Chris Doner Single Slit and Resolution IB Specific Khan Academy Single Slit Interference More on Single Slit

## Resources

 IB Physics Topic 9 Notes IB-Physics.net Chapter 9 Summary IB Revision Notes Isaac Physics Single Slit Level 6 Beyond IB Mr. G 9.2 Teaching Notes 9.2 Student Notes

## Questions

 Cambridge University Press Topic 9: Add Qs Topic 9: Add Qs MS Topic 9: MCQs CUP Website Link Freely available online Dr French's Eclecticon Interference, Doppler, Polarisation Interference, Doppler, Polarisation Solutions Link to Dr French's Site Extension: Pre-University Material Grade Gorilla 9.2 (Single Slits) MCQ Topic 9 (Waves) End Quiz Quick IB Specific Mixed MCQs Mr. G 9.2 Formative Assessment Topic 9 Summary Qs IB Specific Questions

#### Link to Double Slit Diffraction

When performing the double slit experiment, the interference pattern observed often contains characteristics of both the single (bright, wider central maximum) and double slit interference (narrow bright and dark fringes) patterns.

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We often talk about a single slit 'envelope' encompassing the double slit interference pattern.  THe double slit fringes are due to the separation of the two slits, whereas the single slit maxima and minima are due the width of the slit themselves.

Geogebra have a nice simulation that demonstrates the double slit interference pattern inside a single slit envelope. Vary the slider settings and see whether each variable affects the double slit interference pattern, the single slit envelope or both.

## Video Lessons

 Science Shorts Comparison Basics

## Resources

 IB Physics Topic 9 Notes IB-Physics.net Chapter 9 Summary IB Revision Notes Mr. G 9.2 Teaching Notes 9.2 Student Notes

## Questions

 Cambridge University Press Topic 9: Add Qs Topic 9: Add Qs MS Topic 9: MCQs CUP Website Link Freely available online Grade Gorilla 9.2 (Single Slits) MCQ Topic 9 (Waves) End Quiz Quick IB Specific Mixed MCQs Mr. G 9.2 Formative Assessment Topic 9 Summary Qs IB Specific Questions