Summary, Concept Map

Ray Optics

SUMMARY

▪ A ray of light gives the direction of light.

▪ Law of reflection is, i = r

▪ Paraxial rays are the rays travelling close to the principal axis of the mirror and make is small angles with it.

▪ The relation between focal length and radius of curvature in spherical mirror is, 2f = R (or) f = R/2

▪ Cartesian sign conventions are to be followed to trace image formed by spherical mirrors.

▪ The mirror equation is, 1/v + 1/u = 1/f

▪ The magnification in spherical mirror is, m = - h’/h = − v/u,  m = h’/h = (f−v) / f = f / (f – u)

▪ Light travels with lesser velocity in optically denser medium.

▪ Refractive index is the ratio of speed of light in vacuum to speed of light in medium, n= c/υ

▪ Optical path is the equivalent path travelled in vacuum in the same time light travels through a optically denser medium. d' = nd

▪ Law of refraction also called as Snell's law in ratio form is, sin i/sin r = n₂/n₁.

▪ In product form is, n₁, sin i = n₂ sin r

▪ The relative refractive index of second medium with respect to first medium is, n₂₁= n₂/n₁

▪ The apparent depth is always lesser than actual depth. The equation for apparent depth is d’=d/n.

▪ The critical angle of incidence i_c for a ray incident from a denser to rarer medium, is that angle for which the angle of refraction is 90°. For i > i_c, total internal reflection occurs.

▪ Equations for critical angle incidence is, sin i_c = 1/n (or) i_c  = sin^-1(1/n).

▪ Snell's window is the restricted area of circular illumination which appears when seen from water due to critical angle incidence. The radius of the circular illumination is, R = d [1 / √(n² − 1) ] (or) R = d / √(n² − 1)

▪ Optical fibre makes use of critical angle incidence. The acceptance angle in optical fibre is, . Here, n₁, n₂, n₃ are the reflactive indices of core, cladding and surrounding medium respectively.

▪ Glass slabs produce a lateral displacement on the light falling on it. The equation for lateral shift is, L = t [ sin(i−r) /cos(r) ]

▪ The equation for single spherical surface is, (n/v) – (1/u) = (n−1) / R

▪ The focal length of the thin lens is positive for a converging lens and negative for diverging lens. It is not based on the position of the focal point.

▪ The lens makers formula is, 1/f = (n−1) ( 1/R₁ – 1/R₂ )

▪ The lens equation is, 1/v – 1/u = 1/f

▪  The magnification produced by the lens is, m = h’/h =  v/u,  m = h’/h = f  / (f+u) (or) m = h’/h = (f – v) / f  

▪ The power of a lens is a measure of the degree of convergence (or) divergence of light falling on it. Power and focal length are inverse to each other. P = 1/f.

▪ The unit of power is diopter (D) when the focal length is taken in meter.

▪ The effective focal length of lenses in contact is, 1/F = 1/f₁ + 1/f₂

▪ A 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 given by the equation, d = i₁+ i₂  − A

▪ At minimum deviation, i₁ = i₂, r₁ = r₂, and the ray inside the prism is parallel to the base of the prism.

▪ The refractive index of prism depends on angle of prism and angle of minimum deviation given by the equation, n = sin([A+D]/2) / sin(A/2)

▪ When white light travels through a medium, different colours travel with different speeds leading to dispersion of light. Red colour travels faster than violet colour in a medium. In vacuum all the colours travel with the same speed.

▪ The angle of deviation produced by the small angled prism is, δ = (n-1) A

▪ The angular separation between the two extreme colours (violet and red) in the spectrum is called angular dispersion. δ_v − δ_R = (n_V − n_R)A

▪ Dispersive power is the measure of ability of the medium to disperse white light. ω = (n_V – n_R) / (n–1)

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

▪ The scattering of light by particles of size less than wavelength of light is called Rayleigh scattering. The intensity of light produced by Rayleigh scattering is, I ∝ 1/λ⁴

▪ Non-Rayleigh scattering is by suspended dust particles whose size is greater than the wavelength of light. This scattering is independent of wavelength of light.

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