Wave Optics

Objectives

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• The wave aspect of light. • The proof for law of reflection and refraction. • The phenomena like interference, diffraction and polarisation. • The terms like magnification and resolving power etc. • The different optical instruments like microscope, telescope etc

Summary

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„ Light has wave as well as particle nature. „ A wavefront is the locus of points which are in the same state or phase of vibration. Huygen’s principle states the method of propagation of wavefront. „ Light propagating as a wavefront. Point source produces spherical wavefront and source at infinity produces plane wavefront. „ Laws of reflection and refraction are proved by Huygens’ principle. „ The phenomenon of addition or superposition of two light waves which produces increase in intensity at some points and decrease in intensity at some other points is called interference of light. „ If I1 and I2 I a are the intensities of interfering light, then a I I I I I max max ∝ + ( ) = + + 1 2 2 1 2 1 2 2 ; I a a I I I I I min min ∝ − ( ) = + − 1 2 2 1 2 1 2 2 „ If interfering lights have equal intensities of I0 with phase difference ϕ, then I a ∝ ∝  I A      4 2 2 2 2 cos (f / )  I I max = 4 0 when, f p = ±0 2 , ,4p..., Imin = 0 when, f = ±ppp , , ± ± 3 5 ..., „ Two light sources are said to be coherent if they produce waves which have same phase or constant phase difference, same frequency or wavelength monochromatic), same waveform and preferably same amplitude. „ Coherent sources are obtained by wavefront division, intensity division and real and virtual images of light source. „ Young’s double slit uses wavefront division to obtain coherent sources. „ In Young’s double slit experiment, the position of nth bright fringe is, y n D d y n D d = =n l l ( ) or „ In Young’s double slit experiment, the position of nth y dark fringe is, n D d y n D d = n − = ( ) − ( ) 2 1 ( ) 2 2 1 2 l l or „ In Young’s double slit experiment, the equation for bandwidth is, b l = D d „ Interference with polychromatic (white) light produces coloured interference fringes. „ Thin films appear coloured due to interference of white light. „ Transmitted light are, 2µd = nλ; 2 2 1 2 m l d n = − ( ) respectively. „ In thins films the equations for constructive and destructive interference for reflected rays are, 2 2 1 2 m l d n = − ( ) ; 2µd = nλ respectively. „ Diffraction is bending of waves around sharp edges into the geometrically shadowed region. „ A spherical wave front undergoes diffraction in Fresnel diffraction. „ A plane wavefront undergoes diffraction in Fraunhofer diffraction. „ The equation for nth minimum in single slit diffraction is, a sin θ = nλ (nth minimum) „ The equation for nth maximum in single slit diffraction is, a n sin ( q ) l = + 2 1 2 (nth maximum) „ Fresnel’s distance is the distance upto which ray optics is obeyed and beyond which ray optics is not obeyed but, wave optics becomes significant. z a = 2 2l „ Diffraction can also happen in grating which has multiple slits of thickness comparable to wavelength of light used. (a + b) sinθ = m λ; 1 N sin ( q l = = m N or) sinq l m „ Wavelength of monochromatic light and also different colours of polychromatic light can be determined. Using diffraction grating and spectrometer. „ According to Rayleigh’s criterion, for two point objects to be just resolved, the minimum distance between their diffraction images must be in such a way that the central maximum of one coincides with the first minimum of the other and vice versa „ Angular resolution, q l = 1 2. 2 a „ Special resolution, r f a 0 1 22 = . l „ Resolution is measured by the smallest distance which could be seen clearly without „ the blur due to diffraction. „ The phenomenon of restricting the vibrations of light (electric or magnetic field vector) to a particular direction perpendicular to the direction of propagation of wave is called polarization of light. „ If the vibrations of a wave are present in only one direction in a plane perpendicular to the direction of propagation of wave is said to be polarised or plane polarised light. „ The plane containing the vibrations of the electric field vector is known as the plane of vibration. „ The plane perpendicular to the plane of vibration and containing the ray of light is known as the plane of polarisation. „ In plane polarised light the intensity varies from maximum to zero for every rotation of 90° of the analyser. „ If the intensity of light varies between maximum and minimum for every rotation of 90° of the analyser, the light is said to be partially polarised light „ In intensity of transmitted light through two cross polaroids is given by Malus’ Law. I = I0 cos2 θ „ Nicol prism separates ordinary and extraordinary rays by double refraction. „ Light scattered by molecules at perpendicular direction to the incident light is found to be plane polarised. „ A single convex lens can act as a simple microscope when object is within the focal length. „ In near point focusing, the image is formed at D = 25 cm. „ The magnification in near point focusing is, m D f = +1 „ In normal focusing, the image is formed at infinity, the magnification in normal focusing is, m D f = „ The resolving power of microscope is, R d NA M = = 1 2 1 22 min ( ) . l „ The resolving power of telescope is, R r a f T = =1 1 22 0 . l „ Magnification in near point focusing in compound microscope is, m m m L f D f o e o e = =          +           1 „ Magnification in near point focusing in compound microscope is, m m m L f D f o e o e = =                    „ Magnification in astronomical telescope is, m f f o e = and the tube length is, L = f o+ f e „ The correction lens for nearsightedness/myopic eye should be a convex lens with focal length, f = –x. Where x is the near distance upto which it is claearly seen. „ The correction lens for farsightedness/myopic eye should be a concave lens with focal length, f y y = × − 25 25 cm cm . Where, the 25 cm is the near distance. „ The farsightedness arising due to aging is called presbyopia. „ Astigmatism is the defect arising due to different curvatures along different planes in the eye lens.