DIFFRACTION DIFFRACTION John Parkinson ©

Single Slit Diffraction THE BENDING OF WAVES AROUND CORNERS - PAST AN OBSTACLE OR THROUGH A GAP Barrier Ripple Tank Image Single Slit Diffraction Wave Height - Intensity John Parkinson ©

Subsequent position of wavefront WAVEFRONT FORMATION Subsequent position of wavefront “Every point on a wavefront acts as a source of secondary waves which travel with the speed of the wave. At some subsequent time the envelope of the secondary waves represents the new position of the wavefront.” Secondary sources Original wavefront John Parkinson ©

The diffraction grating A prism splits white light up into its various wavelengths A diffraction grating gives a similar result so it is useful when analysing various wavelengths being emitted. Structure: Glass etched with a diamond cutter with 300 lines per mm Each ‘gap’ is only a few wavelengths wide so diffraction occurs at each one John Parkinson ©

n = 1 λ corresponds to a path difference of one wavelength The diffraction grating Each slit effectively acts as a source of secondary waves, which add according to the principle of superposition n= 0 λ n = 1λ n = 2λ n = 1 λ corresponds to a path difference of one wavelength John Parkinson ©

n = 1 when the path difference = 1λ  For light from slits A &B to add constructively, the path difference (AC), equals a whole number of wavelengths. (nλ) Grating Monochromatic light A C Grating element d  B n = 1 when the path difference = 1λ sin θ = AC / AB AB sin  = AC Hence: d sin  = n John Parkinson ©

DIFFRACTION GRATINGS WITH WHITE LIGHT PRODUCE SPECTRA 400nm 500nm 600nm 700nm UV IR John Parkinson ©

A spectrum will result DIFFRACTION GRATING WITH WHITE LIGHT Hence in any order red light will be more diffracted than blue. A spectrum will result Several spectra will be seen, the number depending upon the value of d screen Second Order maximum, n = 2 Grating First Order maximum, n = 1 White Central maximum, n = 0 First Order maximum, n = 1 Second Order maximum, n = 2 John Parkinson ©

Note that higher orders, as with 2 and 3 here, can overlap Be aware that in the spectrum produced by a prism, it is the blue light which is most deviated grating John Parkinson ©

Hence there are 7 orders in all (white central order + 3 on each side) QUESTION 1 Given a grating with 400 lines/mm, how many orders of the entire visible spectrum (400 – 700 nm) can be produced? Finding the spacing d of the “slits” (lines). d = 1/400 = 2.5 x 10-3 mm = 2.5 x 10-6 m n = d sin  n = d sin  /  [sin  = a maximum of 1 at 900] Why do we use 700 nm? Hence there are 7 orders in all (white central order + 3 on each side) John Parkinson ©

For red light in the second order For blue light in the second order Question 2: Visible light includes wavelengths from approximately 400 nm (blue) to 700 nm (red). Find the angular width of the second order spectrum produced by a grating ruled with 400 lines/mm. nλ = d sin θ As before d = 2.5 x 10-6 m nλ = sin θ d For red light in the second order For blue light in the second order 34.1 - 18.7 = 15.40 John Parkinson ©