11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established...

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11: Wave Phenomena 11.3 Single slit diffraction

Transcript of 11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established...

Page 1: 11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established that diffraction will occur at an aperture of width.

11: Wave Phenomena

11.3 Single slit diffraction

Page 2: 11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established that diffraction will occur at an aperture of width.

Single Slit Diffraction

We have already established that diffraction will occur at an aperture of width b if λ ≥ b

When light is shone at a very thin gap (a ‘slit’), it also diffracts. A diffraction pattern is produced on a screen placed a large distance from the slit:

Page 3: 11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established that diffraction will occur at an aperture of width.

Central maximum First minimum

First subsidiary maximum

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Subtitle

Huygens principle: Java applet

http://www.walter-fendt.de/ph11e/huygenspr.htm
Page 5: 11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established that diffraction will occur at an aperture of width.

Explaining The Single Slit Diffraction Pattern

This can be explained if we imagine that all points along the slit width behave as sources emitting secondary wavefronts. (This is called Huygens principle).

If two of these secondary waves meet at a point distant from the slit, they will superimpose upon each other.

Page 6: 11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established that diffraction will occur at an aperture of width.

b

p = point far from the slit.

p

θ

If these two waves are to superimpose upon each other at p then they must meet. However, we assume that the point is so far away that the two waves are approximately parallel.

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First minimum

Darkness is formed. The two waves cancel out.

So the bottom one travels ½ λ further than the top one.

sin θ = ½ λ = λ ½ b b

If θ is very small then sin θ ≈ θ so...

b θ

θ

To first minimum

½ λ

θ = λ b

Page 8: 11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established that diffraction will occur at an aperture of width.

( Extra note:

We know that for appreciable diffraction to take place, λ ≥ b. If λ = b then sinθ=1 so θ would be 90 degrees.

i.e. There are no subsidiary maxima.

This highlights that diffraction is the spreading out of the wave and does not necessarily show interference maxima and minima. )

Page 9: 11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established that diffraction will occur at an aperture of width.

Simulations

Effect of λ on θ: Java applet 1

Java applet 2

Java applet 3

http://www.physics.uoguelph.ca/applets/Intro_physics/kisalev/java/slitdiffr/index.html
http://surendranath.tripod.com/Applets/Optics/Slits/SingleSlit/SnglSltApplet.html
http://www.walter-fendt.de/ph14e/singleslit.htm
Page 10: 11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established that diffraction will occur at an aperture of width.

Experiment

1. Use the laser and single slit to produce a diffraction pattern.

2. Take measurements (including the ‘half width’ d) and thus determine the slit width b. (λred = 700 nm)

b θd

First minimum

Central maximum

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Demo: Diffraction pattern formed by a circular aperture.

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Diffraction from a circular aperture

The angle of the position of the first minimum in this situation is given by the formula...

θ = 1.22 λ b

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Page 14: 11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established that diffraction will occur at an aperture of width.

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Page 15: 11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established that diffraction will occur at an aperture of width.

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Page 16: 11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established that diffraction will occur at an aperture of width.

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Page 17: 11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established that diffraction will occur at an aperture of width.

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Page 18: 11: Wave Phenomena 11.3 Single slit diffraction. Single Slit Diffraction We have already established that diffraction will occur at an aperture of width.

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1AMQ P.H. Regan, Spring 2001 1 n Quanta of Light (4 lectures) –Electromagnetic Waves Spectrum and generation Two slit intereference Single slit diffraction.

1AMQ P.H. Regan, Spring 2001 1 n Quanta of Light (4 lectures) –Electromagnetic Waves Spectrum and generation Two slit intereference Single slit diffraction.

Diffraction & Double Slit Experiment

Diffraction & Double Slit Experiment

Diffraction through a single slit

Diffraction through a single slit

Diffraction at a single slit 11.3.1 Sketch the variation with angle of diffraction of the relative intensity of light diffracted at a single slit. 11.3.2.

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Diffraction -Single Slit

Diffraction -Single Slit

The single slit, diffraction

The single slit, diffraction

Diffraction from a Single Slit

Diffraction from a Single Slit

Topic 9.2 is an extension of Topic 4.4. Both single and the double-slit diffraction were considered in 4.4. Essential idea: Single-slit diffraction occurs.

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Interference & Diffraction 1.Thin Film Interference 2.Double Slit Experiment 3.Single Slit Diffraction 4.Resolution a. Of microscope b. Of human eye 5.

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Topic 9: Wave phenomena -AHL 9.2 –Single-slit diffraction · Topic 9.2 is an extension of Topic 4.4. Both single and the double-slit diffraction were considered in 4.4. Essential

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