Lecture physics a2 diffraction

DIFFRACTION Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016 Contents • Diffraction by a single slit • Diffraction by N slits • Diffraction Grating • X ray diffraction DIFFRACTION • Diffr[.]

DIFFRACTION

Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016

Contents

DIFFRACTION

• Diffraction is the deviation of light from a straight-line path when the light passes through an aperture or around an obstacle

• Diffraction is due to the wave nature of light

wavelets

The position of the wave front at any later time is the envelope of the secondary wavelets at that time

To find the resultant displacement at any point, we combine all the individual displacements produced

by these secondary waves, using the superposition principle and taking into account their amplitudes and relative phases

M

O d

O

M

r

Given a narrow slit of width a

A parallel light beam of wavelength  is

radiated perpendicularly to the slit The beam

is diffracted into many different directions

+ Consider the diffracted rays of angle =0

These rays are focused at F All these rays are in

phase, constructive interference F is a bight

central fringe

+ Consider the diffracted rays of angle 

We draw planes o, 1, 2, each of /2 apart ,

perpendicular to the diffracted rays These

surfaces divide the slit into strips

The width of each band is:

Diffraction BY A SINGLE SLIT

F

M

o

1

S

slit 

/2 sin



 sin 2

The number of bands is: 











 2asin

sin 2

a band

of width

slit of width N

adjacent strips is /2 There is destructive

interference

=>The combined light from 2 adjacent strips is

completely cancels at M

=> If the number of strips is EVEN, M is DARK

M

o

1

S

slit 

/2 sin

5 3;

1)

(2m 2a

λ 1) (2m

sin 1

2m λ

2asin N

: Fringe right

B

3 2;

1;

m a

λ m sin

2m λ

2asin N

: Fringe

Dark













































5 3;

1 2m

2a

λ 1) (2m sin

: Fringe

Bright

3 2, 1, m

a

λ m sin

: Fringe

Dark

0

sin : Fringe Bright

Central































Intensity in the Single-Slit Diffraction Pattern

 





























sin a 2

2 /

2 /

sin I

I

2 o

0083

0 : 0165

0 : 0472

0 : 1

: 7

2 : 5

2 : 3

2 : 1

: I : I : I : I

2 2

2 3

2 1 o

















































Io

I1

I2

+ the central maximum is twice as wide as each side maximum

+

n diffractio no

narrow very

is fringe central

the : λ a

If

5 3;

1 2m 2a

λ 1) (2m sin

: Fringe

Bright

3 2, 1, m

a

λ m sin

: Fringe

Dark

0

sin : Fringe Bright

Central



































Example 36.1 Single-slit diffraction

You pass 633-nm laser light through a narrow slit and observe the diffraction pattern

on a screen 6.0 m away The distance on the screen between the centers of the first minima on either side of the central bright fringe is 32 mm (Fig 36.7) How wide is the slit?

mm 24

.

0 10

32

10 633

6 2 L

d

2 a

a

d 2 sin

d 2 tan

d 2 L

3

9

































d=6.0m