Interference in Physics: Young's Double Slit Experiment and Multiple Slits - Prof. Renat R, Study notes of Advanced Physics

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Physics 102: Lecture 20, Slide 1

• (^) Today’s Lecture will cover

textbook Chapter 35

Physics 113: Lecture 12 Interference Physics 113 Dr. Renat Letfullin

Today

• Theory of Interference

• Examples

• Young’s Double Slit Interference

• Multiple Slits

Physics 102: Lecture 20, Slide 2

Here is how it goes:

Superposition & Interference

• We have seen that when colliding waves combine (add) the result can either be bigger or smaller than the original waves.
• (^) We say the waves add “constructively” or “destructively” depending on the relative sign of each wave. Movie (super) will add constructively will add destructively  (^) In general, we will have both happening

Problem 2.

Two identical loudspeakers separated by a

distance d emit 170 Hz sound waves along

the x-axis. As you walk along the x-axis,

away from the speakers, you don’t hear

anything even though both speakers are on.

What are three possible values for d?

Assume the sound speed is 340 m/s.

Problem 3.

• (^) Two loudspeakers emit sound waves along the x-

axis. The sound has maximum intensity, when

the speakers are 20 cm apart. The sound intensity

decreases as the distance between the speakers is

increased, reaching zero at a separation of 60 cm.

• (^) What is the wavelength of the sound?
• (^) If the distance between the speakers continues to

increase, at what separation will the sound

intensity again be a maximum?

Physics 102: Lecture 20, Slide 13

Young’s Double Slit Key Idea

L

Two rays travel almost exactly the same

distance. (screen must be very far away: L >> d)

Bottom ray travels a little further.

Key for interference is this small extra

distance.

Physics 113 Dr. Renat Letfullin

Physics 102: Lecture 20, Slide 14 d Path length difference =

d 

Young’s Double Slit Quantitative

d sin  Constructive interference Destructive interference (Where m = 0, 1, 2, …) sin(θ)  tan(θ) = y/L Physics 113 Dr. Renat Letfullin

Physics 102: Lecture 20, Slide 16 d Destructive interference dsin (m

Constructive interference dsin^ m where m = 0, or 1, or 2, ...

Young’s Double Slit Quantitative

y sin()  tan() = y/L

d

m L

y



d

m L

y

^ 

L  A little geometry… Physics 113 Dr. Renat Letfullin

Physics 102: Lecture 20, Slide 17 Summary of Young’s Double Slit Concept Screen a distance L from slits Single source of monochromatic light  d 2 slits- separated by d

L

At points where the difference in path length is 0, ,2, …, the screen is bright. (constructive) At points where the difference in path length is the screen is dark. (destructive)

   Physics 113 Dr. Renat Letfullin

Physics 102: Lecture 20, Slide 19 Concept question: Young’s Double Slit

JAVA

Screen a distance L from slits Single source of monochromatic light  d 2 slits- separated by d

1. Constructive
2. Destructive
3. Depends on L The rays start in phase, and travel the same distance, so they will arrive in phase.

L

Light waves from a single source travel through 2 slits before meeting on a screen. The interference will be: Physics 113 Dr. Renat Letfullin

Physics 102: Lecture 20, Slide 20 Screen a distance L from slits Single source of monochromatic light  d 2 slits- separated by d

1. Constructive
2. Destructive
3. Depends on L L ½  shift The experiment is modified so that one of the waves has its phase shifted by ½ . Now, the interference will be: Physics 113 Dr. Renat Letfullin

Concept Example