Diffraction the ability of waves to bend around obstacles Newton tried to explain diffraction due to an attraction between light particles and edge of the obstacle!! In 19 th century, light is understood as a wave by work of Young and Fresnel and scientists searched for other wave phenomena in light. One of them is diffraction.

Diffraction Huygen’s principle requires that the waves spread out after they pass through slits Huygen’s principle requires that the waves spread out after they pass through slits This spreading out of light from its initial line of travel is called diffraction This spreading out of light from its initial line of travel is called diffraction In general, diffraction occurs when wave pass through small openings, around obstacles or by sharp edgesIn general, diffraction occurs when wave pass through small openings, around obstacles or by sharp edges

Diffraction, 2 A single slit placed between a distant light source and a screen produces a diffraction pattern A single slit placed between a distant light source and a screen produces a diffraction pattern It will have a broad, intense central bandIt will have a broad, intense central band The central band will be flanked by a series of narrower, less intense secondary bandsThe central band will be flanked by a series of narrower, less intense secondary bands Called secondary maxima Called secondary maxima The central band will also be flanked by a series of dark bandsThe central band will also be flanked by a series of dark bands Called minima Called minima

Diffraction, 3 The results of the single slit cannot be explained by geometric optics The results of the single slit cannot be explained by geometric optics Geometric optics would say that light rays traveling in straight lines should cast a sharp image of the slit on the screenGeometric optics would say that light rays traveling in straight lines should cast a sharp image of the slit on the screen

Single slit Diffraction Diffraction occurs when the rays leave the diffracting object in parallel directions Diffraction occurs when the rays leave the diffracting object in parallel directions Screen very far from the slitScreen very far from the slit Converging lens (shown)Converging lens (shown) A bright fringe is seen along the axis (θ = 0) with alternating bright and dark fringes on each side A bright fringe is seen along the axis (θ = 0) with alternating bright and dark fringes on each side

Single Slit Diffraction According to Huygen’s principle, each portion of the slit acts as a source of waves According to Huygen’s principle, each portion of the slit acts as a source of waves The light from one portion of the slit can interfere with light from another portion The light from one portion of the slit can interfere with light from another portion The resultant intensity on the screen depends on the direction θ The resultant intensity on the screen depends on the direction θ

Single Slit Pattern w cc sin  c = / w 1. When the wavelength of the light (wave) gets smaller compared to the slit size, the bright spot gets sharper (more particle-like). 2. When ≈ w,  c  90  (more wave-like).

Diffraction Grating The diffracting grating consists of many equally spaced parallel slits The diffracting grating consists of many equally spaced parallel slits A typical grating contains several thousand lines per centimeterA typical grating contains several thousand lines per centimeter The intensity of the pattern on the screen is the result of the combined effects of interference and diffraction The intensity of the pattern on the screen is the result of the combined effects of interference and diffraction

Diffraction Grating, cont The condition for maxima is The condition for maxima is d sin θ bright = m λd sin θ bright = m λ m = 0, 1, 2, … m = 0, 1, 2, … The integer m is the order number of the diffraction pattern The integer m is the order number of the diffraction pattern If the incident radiation contains several wavelengths, each wavelength deviates through a specific angle If the incident radiation contains several wavelengths, each wavelength deviates through a specific angle

Diffraction Grating, final All the wavelengths are focused at m = 0 All the wavelengths are focused at m = 0 This is called the zeroth order maximumThis is called the zeroth order maximum The first order maximum corresponds to m = 1 The first order maximum corresponds to m = 1 Note the sharpness of the principle maxima and the broad range of the dark area Note the sharpness of the principle maxima and the broad range of the dark area This is in contrast to to the broad, bright fringes characteristic of the two-slit interference patternThis is in contrast to to the broad, bright fringes characteristic of the two-slit interference pattern

Diffraction Grating d   r = dsin  = m  Constructive provides much clearer and sharper interference pattern and a practical device for resolving spectra.

Q. A diffraction grating having 20,000 lines per inch is illuminated By parallel light of wavelength 589 nm. What are the angles at Which the first- and second-order bright fringes occur? dsin  = m d = /20000 = 1.27 x (m) First-ordersin   = m /d = 589 x /1.27 x =  1 = 27.6  Similarly, sin  2 = 2 x =  2 = 68.1 

Diffraction occurs when light passes a: Pinhole 2. Narrow slit 3. Wide slit 4. Sharp edge 5. All of the above

nano = x 10 8 = f

X-ray Diffraction and Crystallography

0 th 1 st 2 nd 3 rd 2 nd -order bright fringe 2 nd bright fringe 1 nanometer = 1 x m

Interference in Thin Films Interference effects are commonly observed in thin films Interference effects are commonly observed in thin films Examples are soap bubbles and oil on waterExamples are soap bubbles and oil on water Assume the light rays are traveling in air nearly normal to the two surfaces of the film Assume the light rays are traveling in air nearly normal to the two surfaces of the film

Interference in Thin Films, 2 Rules to remember Rules to remember An electromagnetic wave traveling from a medium of index of refraction n 1 toward a medium of index of refraction n 2 undergoes a 180° phase change on reflection when n 2 > n 1An electromagnetic wave traveling from a medium of index of refraction n 1 toward a medium of index of refraction n 2 undergoes a 180° phase change on reflection when n 2 > n 1 There is no phase change in the reflected wave if n 2 < n 1 There is no phase change in the reflected wave if n 2 < n 1 The wavelength of light λ n in a medium with index of refraction n is λ n = λ/n where λ is the wavelength of light in vacuumThe wavelength of light λ n in a medium with index of refraction n is λ n = λ/n where λ is the wavelength of light in vacuum

Interference in Thin Films, 3 Ray 1 undergoes a phase change of 180° with respect to the incident ray Ray 1 undergoes a phase change of 180° with respect to the incident ray Ray 2, which is reflected from the lower surface, undergoes no phase change with respect to the incident wave Ray 2, which is reflected from the lower surface, undergoes no phase change with respect to the incident wave

Interference in thin films x  s = Difference in two routes + 2x = m  constructive = (2m+1) /2 destructive = 2x (when  i << 1) For an arbitrary angle   s = 2x/cos  Half –reflecting planes x

xn Difference in two routes  s = 2x= mconstructive f Wavelength in the film (not in air) v = c/n = f f c = f f = /n