Wave Optics Class 12 Notes Physics Chapter 10

By going through these CBSE Class 12 Physics Notes Chapter 10 Wave Optics, students can recall all the concepts quickly.

Wave Optics Notes Class 12 Physics Chapter 10

→ Optics is that branch of physics that deals with the nature, sources, properties and effects of light.

→ Light is that form of energy that makes the object visible.

→ Wave optics treat the light as e.m. waves.

→ Light does not require any material medium for propagation.

→ Photographic plates are sensitive to the violet colour and least sensitive to the red colour.

→ Angular fringe width i.e., θ is independent of the distance between the screen and the plane of the slits i.e., D.

→ Speed of light is maximum for violet colour (7.5 × 10¹⁴ Hz) and minimum for red colour (4.3 × 10¹⁴ Hz).

→ Objects are visible from all directions due to the scattering of light.

→ The velocity of light of all wavelengths is the same in free space or vacuum.

→ Hie velocity of light of different colours will be different in media other than vacuum.

→ Our eye fails to see two points separately if they subtend an angle equal to or less than 1 minute and it is called resolving power of the eye.

→ Light of single frequency is called monochromatic.

→ The wavefront due to a point source is spherical and due to a line source, it is cylindrical.

→ The wavefront corresponding to a parallel beam of a light ray is plane.

→ The direction of propagation of light is perpendicular to the wavefront.

→ Each point on a wave point acts as a source of new disturbance and is called a secondary wavelet.

→ Polaroids allow the light oscillations parallel to the transmission axis to pass through them.

→ If the transmission axis of the analyser is perpendicular to that of the polariser, then no light passes through the analyser.

→ If the transmission axis of the polarizer and analyser are parallel, then the whole of the polarised light passes through the analyser.

→ The optical axis is the plane in a polariser or analyser parallel to which the oscillations of light are transmitted through the crystal without change in intensity.

→ Sound waves in the air cannot be polarised as they are longitudinal waves.

→ The tire angle between the direction of propagation and the plane of polarisation or plane of oscillation is 0°.

→ The angle between the direction of oscillation and the direction of propagation is 90°

→ The polarization of light is determined by the change in \(\overrightarrow{\mathrm{E}}\) field vector only.

→ The light is polarised in the plane of incidence by reflection.

→ In the interference, the energy is not destroyed but is redistributed.

→ The sustained interference is obtained by using coherent sources.

→ The order of the central maximum in the interference pattern is zero (i.e., n = 0).

→ When a transparent sheet or film of thickness t is introduced in the path of a ray of light from one slit, the interference pattern is shifted to the same side and an additional path difference of (μ – 1) t is introduced.

→ The interference occurs due to the superposition of wavelets from two wavefronts and the diffraction occurs due to the superposition of wavelets from two parts of the same wavefront.

→ The degree of diffraction is higher for longer wavelengths and thus greater is the deviation of the light waves from the rectilinear path.

→ Due to a lower degree of diffraction, the light waves appear to be travelling in straight lines.

→ The intensity of diffraction fringes decreases as the order of the maximum increases.

→ All interference fringes are of the same intensity

→ Coherent sources can be obtained by reflection, refraction or by the partial reflection of light.

→ Central fringe is always white surrounded by some coloured fringes when monochromatic light is replaced by white light

→ Wavefront: It is defined as the locus of all the particles of a medium vibrating in the same phase,

→ Unpolarised light: It is the light having electric field oscillations in all directions perpendicular to the direction of propagation,

→ Polaroids: They are defined as thin films of ultramicroscopic crystals of quinine idosulphate (called herpathite) with their optic axis parallel to each other.

→ Polarisers: They are defined as the crystals or polaroids on which unpolarised light is incident.

→ Analysers: They are defined as the crystals on which polarised light is incident.

→ Diffraction is the phenomenon of bending waves around the comers of the obstacles or apertures.

→ The resolving power of an optical instrument is its ability to show two closely placed point objects as just separate.

→ Limit of resolution: It is defined as the reciprocal of the resolving power.

→ Fringe Width: It is defined as the spacing between any two consecutive dark or bright fringes. It is denoted by β.

Important Formulae and Laws

→ Doppler’s shift for light is given by :
Δλ = ± \(\frac{λ}{c}\) u
where u is the speed of the source or the observer,
c is the speed of light,
λ is the original wavelength.

→ Malus law:
I = I₀ cos² θ.
where I0 is the intensity of the polarised light incident on the analyser.
θ = angle between the transmission axes of the polariser and analyser.

→ I = \(\frac{\mathrm{I}_{\mathrm{i}}}{2}\) cos² θ
where I_i is the intensity of the unpolarised light incident on the polariser and
I = intensity of the light transmitted through the analyser.
and I₀ = \(\frac{\mathrm{I}_{\mathrm{i}}}{2}\)

→ Polarisation by reflection is given by
μ = tan i_p.
where i_p is the Brewster’s angle

→ Phase difference and path difference (Δx) are related as:
ΔΦ = \(\frac{2 \pi}{\lambda}\) Δx

→ \(\frac{I_{\max }}{I_{\min }}=\frac{\left(a_{1}+a_{2}\right)^{2}}{\left(a_{1}-a_{2}\right)^{2}}\)

→ The fringe width is given by
β = \(\frac{\lambda \mathrm{D}}{\mathrm{d}}\)

→ The location of nth bright fringe on the screen is given by
y_n = nβ = n\(\frac{\lambda \mathrm{D}}{\mathrm{d}}\)

→ The distance of nth dark fringe is given by
y_n = (2n – 1)\(\frac{\lambda}{2 \mathrm{~d}}\)

→ The angular, separation for
1. nth bright fringe is given by
θ_n = \(\frac{\mathrm{n} \beta}{\mathrm{D}}=\frac{\mathrm{n} \lambda}{\mathrm{d}}\)

2. for nth dark fringe :
θn = (2n – 1)\(\frac{\lambda}{2 d}\)

→ Path difference for maximum of interference pattern is :
Δx = 2n\(\frac{λ}{2}\)

→ Path difference for minimum of interference pattern is :
Δx = \(\frac{(2 n+1) \lambda}{2}\)

→ Limit of resolution of telescope is given by
θ = \(\frac{1.22 \lambda}{\mathrm{d}}\)
where d = diameter of the aperture of the objective.

→ The number of fringes and wavelength of light used are related as
n₁λ₁ = n₂λ₂

→ Slit width and intensity are related as
\(\frac{\mathrm{W}_{1}}{\mathrm{~W}_{2}}=\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}\)

→ The amplitude of light wave and the slit width are related as :
\(\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=\frac{\mathrm{A}_{1}^{2}}{\mathrm{~A}_{2}^{2}}=\frac{\mathrm{W}_{1}}{\mathrm{~W}_{2}}\)
or
\(\frac{W_{1}}{W_{2}}=\left(\frac{A_{1}}{A_{2}}\right)^{2}\)

→ Wavelength in a medium is given by
λ’ = \(\frac{λ}{μ}\)

→ Fringe width in the medium of R.I. p is given by
β’ = \(\frac{\lambda^{\prime} D}{d}=\frac{\lambda D}{\mu d}\)

→ Width of central diffraction maximum, β0 = \(\frac{2 \lambda \mathrm{D}}{\mathrm{d}}\)

→ HaLf angular width of central maximum,
θ₁ = \(\frac{λ}{a}\)

→ Fresnel distance,
Z_f = \(\frac{a^{2}}{\lambda}\)

→ R.P. of microscope = 2 \(\frac{\mu \sin \theta}{\lambda}\)

→ Angular limit of resolution of telescope, dθ = \(\frac{1.22 \lambda}{\mathrm{D}}\)

→ Angular position of nth secondary minimum,
θ_n = \(\frac{nλ}{a}\)

→ Distance of nth secondary maximum from centre of screen,
y_n = \(\frac{\mathrm{n} \lambda \mathrm{D}}{\mathrm{a}}\)
where a = slit width.