Chapter 35&36 Interference and the Wave Nature of Light

1. Light as a Wave 2. THE PRINCIPLE OF LINEAR

SUPERPOSITION3. Young's Double-Slit Experiment4. Diffraction

What is physics?

Light as a Wave

Huygens' principle: All points on a wavefront

serve as point sources of spherical secondary wavelets. After a time t, the new position of the wavefront will be that of a surface tangent to these secondary wavelets.

                                                                                                       

       

Constructive Interference

Condition: , m=0, 1, 2, 3, …. 2 1- l l m

Destructive Interference

Condition: , m=0, 1, 2, 3, ….2 11- ( )2

l l m

Young's Double-Slit Experiment

                                                                                                                                                                               

     

Bright fringes:

Dark fringes: 1sin ( )2

l d m

sinl d m

Where m=1, 2, 3, ∙∙∙

Example 1  Young’s Double-Slit Experiment Red light (λ=664 nm in vacuum) is used in Young’s experiment

with the slits separated by a distance d=1.20×10–4 m. The screen in Figure is located at a distance of L=2.75 m from the slits. Find the distance y on the screen between the central bright fringe and the third-order bright fringe.

Interference from Thin Films

         

                   

Condition for destructive interference is:

Diffraction

When waves are incident on an edge, or aperture of size nearly equal to wavelength of the waves, then these waves spread in their direction of travel and undergo interference. These effects are called diffraction.

The diffraction is the bending of waves around obstacles or the edges of an opening.

Diffraction determined by the ratio λ/W

Smaller λ /W, less diffraction Larger λ /W, more diffraction

Note:• X-rays are electromagnetic radiations with

wavelength of the order 0.1nm (compared with 500nm for a typical wavelength of visible light)

• Diffraction gratings: a typical grating might contain N=10,000 slits over a few centimeters equivalent to a grating spacing “d” of a few micrometer.

X-ray Diffraction

• Since x-rays wavelengths are about equal to atomic diameters such grating can not be constructed mechanically.

• In 1912, Max Von Laue showed that a crystalline solid consisting of regular array of atoms might form a natural three dimensional grating for x-rays.

In NaCl, there are unit cells that repeat itself throughout the array. In NaCl, 4 Na ions and 4 Cl ions are associated with each unit cell.

Bragg’s Law

• When a beam of x-rays is incident on a crystal such as NaCl then these x-rays are reflected from different layers (atomic planes). These reflected x-rays are phase coherent. The intensity of reflected beam is maximum at certain angles and minimum at other angles.

Bragg’s Law (Cont.)

• The direction in which reflected rays from any two atomic planes have path difference equal to an integral multiple of wavelength λ, then x-rays interfere constructively, and we get maximum intensity beam.

• The angles are directions for which reflected x-rays from any two atomic planes have path difference λ/2, 3λ/2,… i.e odd integral multiple of λ/2, the rays will interfere destructively. So, beam of minimum intensity is obtained.

Bragg’s Law (Cont.)

• Consider two rays (1) and (2) reflected from upper and lower atomic layers. Ray (2) travels an extra distance BC+CD, so

Path difference = BC + CD ------------ (1)• From triangle ABC and ACD;

BC/AC = Sinθ CD/AC = Sinθ• So, eq (1) becomes;

Path difference = S = ACSinθ + ACSinθ S = 2ACSinθ

Bragg’s Law (Cont.)

• The two rays will interfere constructively, if 2dSinθ = mλ [called Bragg’s relation/law.]

• Where m is the order number of an intensity maximum.• If we have λ, θ and m values then intermolecular spacing “d”

can be calculated.• Also wavelength λ of x-rays can be determined by

λ = (2dSinθ)/m