Diffraction

Diffraction

The spreading out of waves after they pass through a narrow gap or around an obstruction

When is diffraction most noticeable?

When the wavelength of the wave is similar in size to the width of the gap

Single slit diffraction pattern — bright fringes

Areas of maximum intensity caused by constructive interference of parts of the wavefront as it passes through the slit

Single slit diffraction pattern — dark fringes

Areas of zero intensity caused by destructive interference of parts of the wavefront as it passes through the slit

How does the single slit diffraction pattern differ from the double slit pattern?

The single slit has a central maximum that is much wider and brighter than all other fringes; the double slit produces equally spaced fringes of equal intensity

Single slit central maximum features

It has the greatest intensity of any fringe; dark fringes either side have zero intensity; intensity of each subsequent bright fringe decreases moving away from the centre

Effect of increasing wavelength on single slit diffraction pattern

Greater diffraction occurs; the angle of diffraction increases; the bright fringes become wider

Effect of decreasing slit width on single slit diffraction pattern

Greater angle of diffraction; waves spread out more; intensity of maxima decreases; width of central maxima increases; fringe spacing becomes wider

Effect of increasing slit width on single slit diffraction pattern

Less diffraction; fringes become narrower; intensity of central maximum increases

Why does red light produce wider fringes than blue light in single slit diffraction?

Red light has a longer wavelength so it is diffracted more, increasing the angle of diffraction and producing wider fringes

Single slit diffraction with white light — central maximum

Bright white, because all wavelengths interfere constructively at the centre; much wider and brighter than all other fringes

Single slit diffraction with white light — other maxima

All other maxima are composed of a spectrum; violet/blue nearest the centre (diffracted least); red furthest from the centre (diffracted most); colours appear blurry and spectra eventually merge

Single slit white light intensity pattern features

Central maximum equal in intensity to monochromatic light; non-central maxima are wider and less intense; fringe spacing between maxima gets smaller further from centre; red wavelengths increase and blue wavelengths decrease with increasing order n

Combined single slit and double slit intensity pattern

The double slit produces equally spaced fringes of equal intensity; the single slit produces a broad central maximum envelope; the combined pattern has equally spaced bright fringes modulated by the single slit envelope

What property of a wave does NOT change during diffraction?

The wavelength — only the amplitude changes when a wave is diffracted

When drawing diffracted waves, what must you keep constant?

The wavelength (distance between wavefronts); only the amplitude changes

X-rays and crystalline solids — why diffraction occurs

X-ray wavelengths (10⁻⁸ to 10⁻¹³ m) are similar in size to the gaps between atoms in a crystalline solid, so significant diffraction occurs

Diffraction grating

An optical device consisting of a large number of very thin, equally spaced parallel slits carved into a glass plate; used to diffract light into bright and dark fringes or separate white light into its component wavelengths

Why are diffraction gratings more useful than double slits?

They produce sharper patterns — the bright fringes are narrower and brighter, and the dark regions are wider and darker

Diffraction grating equation

d sin θ = nλ, where d = slit spacing (m), θ = angle of diffraction from the normal (°), n = order of maximum, λ = wavelength (m)

Variables in the diffraction grating equation

d = distance between adjacent slits (m); θ = angle between the normal and the nth order maximum; n = order of maxima (0, 1, 2, 3…); λ = wavelength of light (m)

Slit spacing d from number of lines per metre N

d = 1/N; if N is in lines/mm then d is in mm; if N is in lines/m then d is in m

Angular separation of maxima

The angle θ is measured from the centre (the normal); higher orders of n occur at greater angles; angular separation between two orders = θ₂ − θ₁

Maximum order of maxima visible

Occurs when θ = 90°, so sin θ = 1; maximum order n = d/λ; if this gives a decimal, round down to the nearest integer

Derivation of diffraction grating equation — path difference at nth order

Path difference at zeroth order = 0; at first order = λ; at nth order = nλ; using trigonometry: sin θ = nλ/d, rearranged to d sin θ = nλ

Diffraction gratings in spectrometers — uses

Analysing light from stars; determining the composition of stars; measuring red shift or rotation of stars; measuring wavelength/frequency of starlight; chemical analysis; analysing absorption/emission spectra

Diffraction gratings in X-ray crystallography

X-rays directed at a thin crystal sheet act as a diffraction grating; since X-ray wavelengths ≈ atomic spacing, a diffraction pattern forms; used to measure atomic spacing in materials

Diffraction gratings in monochromators

Used to isolate a specific wavelength of light to analyse molecules in diseased cells (biopsy samples) or to excite molecules in a sample with a particular wavelength

Diffraction gratings in optical fibres

Used to select the optimum wavelength of light for transmission through an optical fibre