Summary, Concept Map

Wave Optics

SUMMARY

▪ 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 are the intensities of interfering light, then I_max = I₁ + I₂ + 2√(I₁1₂); I_min = I₁ + I₂ − 2√(1₁1₂)

▪ If interfering lights have equal intensities of I₀ with phase difference ϕ, then

I ∝ 4a² cos² (ϕ /2)  [I ∝ A²]

I_max = 4I₀  when, ϕ = 0, ±2π, 4 π..,

I_min = 0  when, ϕ = ±π, ±3π, ±5π,..,

▪ 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 n^th bright fringe is, y_n = n [ λD/d]

▪ In Young's double slit experiment, the position of nth dark fringe is, y_n = [(2n-1)/2] [ λD/d]

▪ In Young's double slit experiment, the equation for bandwidth is, β = [ λD/d]

• Interference with polychromatic (white) light produces coloured interference fringes.

• Thin films appear coloured due to interference of white light.

• Transmitted light are, 2μd = μλ; 2µd = (2n-1) [λ/2] respectively.

• In thins films the equations for constructive and destructive interference for reflected rays are, 2µd = (2n-1) [λ/2]; 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 (n^th minimum)

• The equation for nth maximum in single slit diffraction is, a sin θ = (2n+1) λ/2 (n^th 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 = a² / 2λ

• Diffraction can also happen in grating which has multiple slits of thickness comparable to wavelength of light used. (a + b) sin θ = m λ; sin θ = Nmλ

• 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, θ = 1.22λ / a

▪ Special resolution, r₀ = 1.22 λ f / a

▪ 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 cos²θ

▪ 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 = 1+ D/f

▪ In normal focusing, the image is formed at infinity, the magnification focusing is, m = D/f

▪ The resolving power of microscope is, R_M = 1/d_min = 2(NA) / 1.22λ

▪ The resolving power of telescope is, R_T =  1/r₀ = a/ 1.22λf

▪ Magnification in near point focusing in compound microscope is, m = m_om_e = (L/f₀)(1 + D/f₀)

▪ Magnification in astronomical telescope is, m = f_o/f_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×25cm / y−25cm. 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.

SUMMARY

• In ray optics, light is treated as a ray in the direction of light.

• Light undergoes reflection at polished surfaces and it is governed by laws of reflection.

• In general, plane mirrors form virtual and laterally inverted images at equal distance inside the mirror.

• The height of plane mirror needed to see a person fully in a mirror is half of the height of person.

• Spherical mirrors form a part of a sphere.

• Paraxial rays are the rays travelling close to the principal axis of the mirror and make small angles withit.

• There is a relation between f and R in spherical mirrors for paraxial rays.

• Image formation in spherical mirrors is based on mirror equation.

• There is a set of Cartesian sign conventions to be followed to trace image formed by spherical mirrors.

• Light travels with lesser velocity in optically denser medium.

• Optical path is the equivalent path travelled in vacuum in the same time light travels through a optically denser medium.

• The phenomenon of refraction is governed by laws of refraction (Snell’s law).

• The apparent depth is always lesser than actual depth.

• Refraction takes place in atmosphere due to different layers of air with varying refractive indices.

• Total internal reflection takes place when light travels from denser to rarer medium with the angle of incidence greater than critical angle.

• There are several applications of total internal reflection.

• A glass slab produces lateral displacement or shift of ray entering into it.

• Thin lenses are formed by two spherical refracting surfaces.

• The image tracing in thin lenses is done with the Cartesian sign conventions and with the help of lens equation.

• Power and focal length are inverse to each other.

• There is effective focal length for lenses in contact and out of contact.

• Prism produces deviation on the incident ray.

• Angle of deviation depends on angle of prism, angle of incidence and refractive index of material of prism.

• The refractive index of prism depends on angle of prism and angle of minimum deviation.

• When white light travels through a medium, different colours travel with different speeds leading to dispersion of light.

• Dispersive power is the measure of ability of the medium to disperse white light.

• Rainbow is formed by dispersion of light by droplets of water.

•Light can be scattered by the particles present in atmosphere.

• The scattering of light by particles of size less than wavelength of light is called Rayleigh scattering which is inversely proportional to fourth power of wavelength.

• If the scattering is by suspended dust particles whose size is greater than wavelength of light, the scattering is independent of wavelength.

• There are four theories on light each explaining few aspects of light.

• Light has wave and particle nature.

• In wave optics we treat light propagating as a wavefront.

• Huygens’ principle explains the propagation of light as wavefront.

• Laws of reflection and refraction are proved by Huygens’ principle.

• In interference, two light waves are added to get varying intensities at different points.

• Coherent sources produce monochromatic light waves in phase or with constant phase difference.

• Coherent sources are obtained by intensity division, wavefront division and real and virtual images of light source.

• Young’s double slit uses wavefront division to obtain coherent sources.

• Interference with polychromatic (white) light produces coloured interference fringes.

• Thin films appear coloured due to interference of white light.

• Bending of light around sharp edges is called diffraction.

• There are two types of diffractions called Fresnel and Fraunhofer diffractions

• Diffraction takes place at single slit which has a width comparable to the wavelength of light.

• Fresnel’s distance is the distance up to which ray optics is obeyed.

• Diffraction can also happen in grating which has multiple slits of thickness comparable to wavelength of light used.

• Using diffraction grating and spectrometer wavelength of monochromatic light and also different colours of polychromatic light can be determined.

• Resolution is the quality of image which is decided by diffraction effect and Rayleigh criterion.

• Resolution is measured by the smallest distance which could be seen clearly without the blur due to diffraction.

• Polarisation is restricting electric or magnetic field vibrations to one plane.

• Polarisation is obtained by selective absorption, reflection, double refraction and scattering.

• Malus’ law gives the intensity of emerging light when a polarised light enters two polaroids kept at an angle.

• Brewster’s law relates angle of polarisation and refractive index of the medium.

• Optically active crystals can be classified as uniaxial and biaxial crystals.

• When light enters in to optically active crystals, double refraction takes place.

• In double refraction, ordinary ray obeys laws of refraction and extraordinary ray does not obey laws of refraction.

• Nicol prism separates ordinary and extraordinary rays by transparent cement called Canada balsam.

• Light scattered by molecules at perpendicular direction to the incident light is found to be plane polarised.

• Single convex lens can act as a simple microscope when object is within the focal length.

• Two focusing namely, near point focusing and normal focusing are possible.

• In near point focusing, the image is formed at 25 cm which is the distance of distinct vision for normal eye. Whereas, in normal focusing the image is formed at infinity.

• To find magnification in near point focusing we use lateral magnification and for normal focusing we use angular magnification.

• Resolution of microscope could be improved by using oil immersed eye piece.

• Compound microscope has improved magnification.

• Astronomical telescope has an eye piece of long focal length and eye piece of short focal length.

• Terrestrial telescopes have one addition lens for producing erect image.

• Reflecting telescopes have advantages as well as disadvantages.

• Eye has three problems (i) nearsightedness, (ii) farsightedness, (iii) astigmatism.

CONCEPT MAP