DIFFRACTION Shrishail Kamble

True, to a point. On a much smaller scale, when light waves pass near a barrier, they tend to bend around that barrier and spread at oblique angles. This phenomenon is known as diffraction of the light, and occurs when a light wave passes very close to the edge of an object or through a tiny opening, such as a slit or aperture. In his 1704 treatise on the theory of optical phenomena (Opticks), Sir Isaac Newton wrote that "light is never known to follow crooked passages nor to bend into the shadow". He explained this observation by describing how particles of light always travel in straight lines, and how objects positioned within the path of light particles would cast a shadow because the particles could not spread out behind the object.

Diffraction is a wave effect Interference pattern of light and dark bands around the edge of the object. Diffraction is often explained in terms of the Huygens principle, which states that each point on a wavefront can be considered as a source of a new wave. 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 wavefronts

Diffraction by a Single Slit or Disk If light is a wave, it will diffract around a single slit or obstacle. Figure 35-1. If light is a wave, a bright spot will appear at the center of the shadow of a solid disk illuminated by a point source of monochromatic light.

What is diffraction? Diffraction is the bending of light around the sharp edges of an obstacle in order and produces bright illumination in geometrical shadow region. Diffraction becomes significant only when the obstacle size is comparable with wavelength of incident light.

Distinguish between Fresnel & Fraunhoffer diffraction Fresnel Diffraction Fraunhoffer Diffraction The source and the screen are at finite distance from the obstacle. The source and the screen or both are effectively at infinite distance from the obstacle. Observation of Fresnel diffraction does not require any lenses. The conditions required for the Fraunhoffer diffraction are achieved using two convex lenses.

Fraunhoffer Diffraction Fresnel Diffraction Fraunhoffer Diffraction Incident wave fronts are cylindrical. Incident wave fronts are planar. The phase of the secondary wavelets is not the same at all the points in the plane of the obstacle. The phase of the secondary wavelets are the same at all the points in the plane of the obstacle. It is experimentally simple but the mathematical analyses is complex. This diffraction is simple to handle mathematically because the rays are parallel.

Resolving Power The ability of an optical instrument to produce separate patterns of two close objects is known as resolving power.

Just Resolved Rayleigh’s Criterion of Resolution According to Rayleigh criterion, two point sources are resolvable by an optical instrument when the central maximum in the diffraction pattern of one falls over the first minimum in the diffraction pattern of the other and vice versa. Just Resolved

Let us consider the resolution of two wavelengths λ1 & λ2 by a grating Let us consider the resolution of two wavelengths λ1 & λ2 by a grating. The difference in wavelengths is such that their principal maxima are separately visible. There is distinct point of zero intensity in between the two. Hence the two wavelengths are well resolved. Well Resolved

Again consider the case when difference in wavelengths is so small that the central maxima corresponding to two wavelengths come closer as shown in figure. The resultant intensity in this case is quite smooth without any dip. This condition is known as not resolved. Not Resolved

Diffraction Grating

Diffraction Grating is an optical device used to study the different wavelengths contained in a beam of light. The device usually consists of thousands of narrow, closely spaced parallel slits (or grooves). A transmission grating can be made by ruling parallel lines on a glass plate with a fine diamond point. Number of lines ruled is generally ≈ 15,000 – 30,000 lines per inch. The spaces between the lines are transparent to the light and hence act as separate slits.

Grating Constant cm cm a: width of transparent part b: width of opaque region Grating element = (a + b)   cm   cm

Theory of Transmission Grating Let XY is the grating surface & MN is the screen, both are perpendicular to the paper. AB is the slit and BC is the opaque portion. The width of slit is a and the opaque spacing between any two consecutive slit is b. Let a plane wavefront be incident on the grating surface. The point P will be central maximum.

Consider the secondary waves travelling in a direction inclined at an angle θ with the direction of the incident light. The intensity at point P1 will depend on the path difference between the secondary waves originating from the corresponding points A and C. Path difference = AC Sinθ = (AB + BC) Sinθ = (a + b) Sinθ

Let, λ and λ + dλ: two nearby wavelengths present in incident light.   If the incident light consists of more than one wavelength, the beam gets dispersed and the angle of diffraction for different wavelength will be different. Let, λ and λ + dλ: two nearby wavelengths present in incident light. θ and θ + dθ: angles of diffraction corresponding to these two wavelengths.

Resolving power of diffraction grating The R.P. of grating is defined as the, ratio of wavelength λ of any spectral line to the smallest difference in wavelength dλ, between this line and a neighboring line such that the two lines appear just resolved, according to Rayleigh’s criterion.  

Let a beam of light having two wavelengths λ and λ+dλ is normally incident on the grating. XY = filed of view of the telescope i.e. screen, P1 = nth primary maxima of spectral line of wavelength λ at any angle of diffraction θn. P2 = nth primary maxima of spectral line of wavelength λ+dλ at any angle of diffraction θn+ dθn.

This is possible if the extra path difference is λ/N. The direction of the nth primary maximum for a wavelength λ is given by,   ..... (1) The direction of the nth primary maximum for a wavelength λ+dλ is given by,   ..... (2) These two lines appear just resolved if the angle of diffraction (θn + dθn) also corresponds to the direction of the first secondary minimum after the nth primary maximum at P1. This is possible if the extra path difference is λ/N. where, N – total number of lines on grating surface.

Equating R.H.S. of eqn (2) and (3)   ..... (3) Equating R.H.S. of eqn (2) and (3)     Thus, the resolving power of a grating is independent of the grating constant. The resolving power is directly proportional to, The order of spectrum and The total number of lines on the grating surface.

The penetration of waves into the regions of geometrical shadow is ------------- Interference b) polarization c) diffraction d) dispersion In Fraunhoffer diffraction the wavefront undergoing diffraction has to be ---------------- Spherical b) cylindrical c) elliptical d) plane Maximum number of orders possible with a grating is----------------- Independent of grating element Directly proportional to the grating element inversely proportional to the grating element Directly proportional to the wavelength

The criterion of resolution of optical instruments was given by -------- a) Newton b) Huygen c) Rayleigh d)Ramsden The resolving power of grating having N slits in nth order will be------ a) (N+n) b) (N-n ) c) nN d) n/N When white light is incident on diffraction grating, the light diffracted more will be ----------- a) Blue b) violet c) red d) yellow In Fresnel diffraction, the distance of the source of light & the screen or both from the obstacle is -------------- a) Infinite b) finite c) 10m d) none of these

In Fraunhoffer diffraction, the distance of the source of light & the screen from the obstacle is -------------- a) Infinite b) finite c) 10m d) none of these The grating constant is given by the equation ---------------- a)No. of lines per cm c)2.54/ No. of lines per cm b) No. of lines per inch d) 1/No. of lines per cm The resolving power of a grating is --------------- λ/dλ b)dλ/λ c) nN/ dλ d)n(n+1) The resolving power of a grating is directly proportional to -------- a)wavelength b)slit width c) distance of screen from grating d) order of the spectrum

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