1.1. To understand diffraction gratingsTo understand diffraction gratings

2.2. To understand how changing wavelength To understand how changing wavelength and slit size affect the transmitted patternand slit size affect the transmitted pattern

3.3. To understand how the diffraction grating To understand how the diffraction grating equation is derivedequation is derived

4.4. To be able to complete diffraction grating To be able to complete diffraction grating related calculationsrelated calculations

Book Reference : Pages 205-207Book Reference : Pages 205-207

A diffraction grating is plate with many parallel A diffraction grating is plate with many parallel slits in it. slits in it.

1.1. Light passing through each slit is diffractedLight passing through each slit is diffracted

2.2. The Diffracted light wave from adjacent slits The Diffracted light wave from adjacent slits interfere, (reinforce each other) in certain interfere, (reinforce each other) in certain directions onlydirections only

1.1. The central beam is The central beam is referred to as the “zero referred to as the “zero order beam”order beam”

2.2. The other beams are The other beams are numbered outwards on numbered outwards on each side: 1st order, 2nd each side: 1st order, 2nd order etcorder etc

1.1. How does the diffraction pattern change How does the diffraction pattern change with wavelength?with wavelength?

2.2. How does the diffraction pattern change How does the diffraction pattern change with slit distance? with slit distance?

Virtual Physics Lab : Waves Virtual Physics Lab : Waves Diffraction Diffraction

1.1. How does the diffraction pattern change How does the diffraction pattern change with wavelength?with wavelength?

2.2. How does the diffraction pattern change How does the diffraction pattern change with slit distance? with slit distance?

The angle of diffraction between each beam and The angle of diffraction between each beam and the zero order beam the zero order beam increasesincreases with with increasingincreasing wavelengthwavelength (Blue to Red) (Blue to Red)

The angle of diffraction between each beam and The angle of diffraction between each beam and the zero order beam the zero order beam increasesincreases with with decreasing decreasing gap sizegap size

1.1. Each diffracted Each diffracted wavefront reinforces an wavefront reinforces an adjacent wavefrontadjacent wavefront

2.2. Wavefront at P reinforces Wavefront at P reinforces wavefront at Y one cycle wavefront at Y one cycle earlier which in turn earlier which in turn reinforces wavefront at R reinforces wavefront at R one cycle earlierone cycle earlier

3.3. This forms a new This forms a new wavefront PYZ which wavefront PYZ which travels in a certain travels in a certain direction and forms a direction and forms a diffracted beamdiffracted beam

θ

θ

P

Q

Y

d

Formation of nFormation of nthth order beam order beam

Wavefront at P reinforces Wavefront at P reinforces wavefront from Q emitted n wavefront from Q emitted n cycles earlier.cycles earlier.

Wavefront from Q has Wavefront from Q has travelled n wavelengths.travelled n wavelengths.

QY is nQY is nλλ

sin sin θθ = QY/QP = QY/QP (substitute)(substitute)

sin sin θθ = = nnλλ /d/d (rearrange)(rearrange)

dsin dsin θθ = n = nλλWhere d is the slit separation, n is the order of the diffracted beam and λ is the wavelength

NotesNotes

The number of slits per metre N is 1/dThe number of slits per metre N is 1/d

As d decreases the angle of diffraction As d decreases the angle of diffraction increases. (As N increases, the angle of increases. (As N increases, the angle of diffraction increases)diffraction increases)

Maximum number of orders is when Maximum number of orders is when θθ = 90° = 90° and hence sin and hence sin θθ = 1 = 1

∴∴n = d/n = d/λλ

(Rounded (Rounded downdown to the nearest whole number) to the nearest whole number)

A laser of wavelength 630nm is directed normally A laser of wavelength 630nm is directed normally at a diffraction grating with 300 lines per mm. at a diffraction grating with 300 lines per mm. Calculate :Calculate :

a)a) The angle of diffraction for the first two The angle of diffraction for the first two orders orders [10.9° & 22.2°][10.9° & 22.2°]

b)b) The number of diffracted orders produced The number of diffracted orders produced [5][5]

Light incident normally on a diffraction grating Light incident normally on a diffraction grating with 600 lines per mm contains wavelengths of with 600 lines per mm contains wavelengths of 580nm and 586nm only. 580nm and 586nm only.

a)a) How many diffracted orders are seen in the How many diffracted orders are seen in the transmitted light transmitted light [2][2]

b)b) For the highest order calculate the angle For the highest order calculate the angle between the two diffracted beams between the two diffracted beams [0.58°][0.58°]

Light of wavelength 480nm is incident normally on Light of wavelength 480nm is incident normally on a diffraction grating the 1a diffraction grating the 1stst order transmitted order transmitted beams are at 28° to the zero order beam. beams are at 28° to the zero order beam. Calculate: Calculate:

a)a) The number of slits per mm for the grating The number of slits per mm for the grating [1092][1092]

b)b) The angle of diffraction for each of the other The angle of diffraction for each of the other diffracted orders diffracted orders [69.9°][69.9°]