D Sin   K  , D Is The Distance Between Two Man Nodes

If the number of slots is narrow

N = 3 (odd number ̉ ) then the light oscillations due to the two slits

The narrow slit sent will cancel out the u, and the light oscillation caused by the third slit will

not destroyed . The result is between two poles .

the pole is a pole

Maybe you are interested!

yes

Pole

D Sin   K  , D Is The Distance Between Two Man Nodes

This belt has a fairly small magnitude , so it is suitable for

call

is pole

band

extra .

Clear between the poles

this big guy and the two poles

right side main

There are two extremes .


It has been proven that if there are N narrow gaps between two circles , then

pole

The main circuit will have N -1 poles .

small and N-2 pole

husband

Figure 3.24 represents

diffraction pattern through three narrow slits and the position of the maxima and minima. If N is large, the width of the main maxima is narrow, and the main maxima observed will be sharp. Because the secondary maxima are much less bright than the main maxima, we do not need to pay attention to them and the diffraction pattern through many narrow slits will be a series of parallel, evenly spaced bright lines. From the formula () we see: to observe the main maxima, then d ( because sin 1) .

3.4.3. Diffraction grating


a. Concept

A diffraction grating is a system of many identical narrow slits of width b , lying parallel and equidistant on the same plane. The distance d between two consecutive slits is called the period of the grating.

b. Classification

There are two types of diffraction gratings: reflection gratings and transmission gratings.

3.4.4. Diffraction on crystals


The constituent atoms (molecules or ions )


Figure 3.25. Diffraction grating


Figure 3.26.


so crystalline solid can be


about to

arranged in a periodic structure called

is a crystal lattice in which the positions of the

atoms (molecules or ions ) are called lattice nodes. The distance between lattice nodes,

characteristic for periodicity , which is

call

is the period of the crystal lattice. Projected onto

a single beam of X-rays , each node of the network becomes how many

far and

The crystal lattice acts as a self-healing mechanism with the period being the period of the crystal lattice .

The X-ray beam will radiate in many directions, but only in

direction of reflection (direction where the angle of reflection is equal to the angle of incidence), the intensity of


how many

far enough away to see clearly

how much

far

Consider the diffracted rays in the direction of mirror reflection. The optical path difference between the two reflected rays on the two planes 11' and 22' is:

2d sin (3.24)

The optical path difference between two reflected rays on two planes 11' and 33' is 2 . Thus, according to the mirror reflection method, there will be



Figure 3.27. Diffraction on crystals

a diffracted beam with optical path differences of, 2 , 3 , ... , the rays

far away

will interfere with each other and give a diffraction maximum if two successive diffracted rays have a path difference equal to an integer number of wavelengths :

2d sin k


or:


sin k , (3.25)

2d


with d being the distance between two atomic planes of the crystalline solid (the period of the crystal lattice). The formula ( 3.25) is called the Vulf-Bragg formula. This is the basic formula for analyzing the structure of crystalline solids by X- rays . If

know the wavelengthof X-rays and angle measurement we can determine

d means to determine the structure of the crystal lattice.

period


1. Present gratitude


how much

CHAPTER 3 SUMMARY


away from light

The phenomenon of light rays being deviated from rectilinear propagation when passing near objects

small enough obstacle

2. Huygens - Fresnel principle:

a. Statement

call

is a present

how much

light radiation


Lip

point in space

light waves from real sources

send to

All become secondary light sources that emit light waves forward .

The amplitude and phase of the secondary source are the amplitude and phase given by the actual source.


cause

out of ear

location of the source

b. Expression of the resulting wave at M

x dx ( M ) A ( , 0) cos ( t r 1r 2) dS


( S )


3. Fresnel sphere method

r 1 r 2v


The total amplitude due to the Fresnel zones at M is:

a a 1 a 2 a 3 a 4 a 5 a 6 ...


4. How far is the spherical wave through the round hole?


Pressure

By using the Fresnel bridge method , we can calculate

amplitude of light

general morning

ears

M, distance R from source S :

a a 1a n ,

2 2


The sign "+" corresponds to odd n, the sign "-" corresponds to even n.

Consider the cases:

When there is no screen P or the size of the circular hole is very large n : n , a n 0

should be the brightness of ear M:

2 a 2

I 0 ka

k1.

4

If the hole contains the required odd number :

I ka 2 k ( a 1 a n ) 2 I ,

2 2 0


Point M is brighter without screen P.

In particular, if the hole is a single demand: n = 1 a a 1


1

0

Ika24 I .

The light intensity is 4 times higher than without the hole, so point M is very bright.

If the hole contains an even number , request:

I ka 2 k ( a 1 a n ) 2 I ,

2 2 0


Point M is darker when there is no circular hole.

In particular, if the circular hole contains two spheres then : a a 1 a 2


0I0 ,

2 2

Point M is completely dark.


After

Point M may be brighter or darker than without the hole .

depending on the size of the hole and the position of the viewing screen.


5. How far is the spherical wave passing through the circular disk?


The amplitude of light oscillation at M is:

a a m 1 a m 2 a m 3 a m 4 a m 5 ...

a a m 1

2


I ka 2 k ( a m 1 ) 2 k ( a 1 ) 2 I .

2 2 0


So:If the disk only covers a small part of the zone, then at M we always have a bright spot with a light intensity slightly less than the light intensity at M in the absence of an occluding object.

6. How much?

propagation of a plane wave through a narrow slit

Pressure

By using Fresnel bridge method we can calculate

knife amplitude

total luminosity

ears

a point M on the observation screen.


As a result , we have the following extreme conditions:

big, big

small

narrow slit radiation

Pole

band

between :

sin 0


Pole

how much

distant:

sin ; 2 ;

bb

3

b


; ...


Pole

band

how much

distant:

sin 3 ; 5 ; 7 ; ...

2b 2b 2b


On the intensity distribution graph we see the pole

band

very bright , the

pole

band

how much

radiation of order k = 1,2,3... lying between the poles

how much

radiation and

bilateral symmetrical distribution

band

keep a . pole

band

between the two widths

pair of poles

band

different. According to theoretical calculations, the luminous intensity of the

pole

band

how much

radiation follows the following formula :

I 0 : I 1 : I 2 : I 3 : ... 1: 0, 045 : 0, 016 : 0, 008 : ...


7. Diffraction on crystals

For crystalline solids, the crystal lattice plays an indispensable role .

three-dimensional space. The many

X - ray radiation on the man buttons

g gives us the result :

2d sin k , d is the distance between two mandrels

g , is called the lattice constant. This

is the Vulf-Bragg formula, which is used to determine the structure of crystalline solids.

THEORETICAL QUESTIONS


1. Define

present gratitude

how much

away from light. Using Huygens' principle

qualitative explanation of the present

how much

distant.

2. State the Huygens-Fresnel principle.

3. Present the Fresnel sphere method: how to divide the zone, calculate the light intensity and the total amplitude.

4. Current survey

how much

light through a small round hole and through a disc

circle, state the difference between the two phenomena above.


5. Describe the current situation

how much

light through a narrow slit

. Find conditions

pole

big, big

how much

diffraction pattern of a plane wave passing through a

narrow gap

6. Investigate the diffraction through N slits of a plane wave, define the main and secondary minima, main and secondary maxima. Draw the diffraction pattern of a plane wave through three narrow slits, indicating the positions of the maxima and minima.

7. Present much

X- ray scattering on crystals. Vulf - Bragg formula. State

application

g of the present

how much

X - ray

CHAPTER 3 EXERCISES


Lesson 3.1.

A light source S emits monochromatic light with a wavelength of 550nm , shining on a screen E 11m away from S. At the point between screen E and source S there is a screen containing a circular hole with a diameter of 4.2mm . Indicate whether the brightness at the center of the diffraction pattern obtained on the screen is greater or less than the brightness at that spot without the screen.

Lesson 3.2.

Monochromatic light has a wavelength of 500nm , shining perpendicularly into a slit with a width of 0.02mm . Find the width of the slit image on a screen placed 1m from the slit (the lens is placed close to the slit).

Lesson 3.3.

A parallel beam of light with a wavelength of 500nm is irradiated perpendicularly to a diffraction grating. A converging lens is placed near the grating. The distance from the screen to the lens is 1m . The distance between the two maximum lines of the first-order spectrum is 20.2cm . Determine:

a. Period d of the grating.

b. Number of lines per mm of grating.

Lesson 3.4.

Shine a chromatic light with wavelength = 0.5m into a circular hole with radius

unknown. The point light source is placed 2m away from the circular hole , and an observation screen is placed 2m behind the circular hole . What is the radius of the circular hole so that the center of the diffraction pattern is the darkest?

Lesson 3.5.

A point light source shines a monochromatic light with wavelength = 0.5 m into a circular hole with radius r = 1mm . The distance from the light source to the circular hole is R = 1m. Find the distance from the circular hole to the observation screen so that the circular hole contains three Fresnel lenses .

Lesson 3.6.

A good screen


placed at a wavelength distance from the light source

=0.5 m at a distance of 2m . A round hole is placed between the screen and the light source.

diameter 0.2cm . Find the number of Fresnel spheres that the circular hole cannot fit .

Lesson 3.7.


Place an observation screen ̛ n away from a point light source emitting measured light.

wavelength = 0.6 m in a distance x . In the middle of the distance x , place a disc

round

small opaque object with diameter 1mm . What is x so that point M is 0 on the screen?

The observation has a brightness similar to that of a circular object, knowing that point M is 0.and source

light is evenly distributed on the axis

Lesson 3.8.

door

round.

A parallel beam of light with wavelength λ = 0.589m is projected straight

angle with a narrow slit of width b=2 m . Ask which diffraction minima are

observe from any angle

Lesson 3.9.

how far? ( compared to the original position )


Shine a parallel, sharp beam of light perpendicular to a narrow slit .

The wavelength of light is 16 times the width of the slit .

. Ask for the first diffraction minimum

At what angle is the three objects observed ?

Lesson 3.10.

A beam of light is


perpendicular to a line from a certain angle . Knowing that the angle

how much

The distance for the spectral distance λ 1 =0.65 m in the second-order spectrum is

φ 1 =45 0 . Determine the angle of the third order spectrum.

Lesson 3.11.

far infrared with spectral density λ 2 = 0.5 m


Given a plane circuit with period d = 2μm . After the circuit , place a

converging lens,

on the observation screen placed at the focal plane of the human lens

We observe that the distance between the two first- order spectra corresponds to the wavelength

λ 1 = 0.4044μm and λ 2 = 0.4047μm equals 0.1mm . Determine the focal length of the lens.

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