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 Ii 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 ip.
where ip 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
yn = nβ = n$$\frac{\lambda \mathrm{D}}{\mathrm{d}}$$

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

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

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,
Zf = $$\frac{a^{2}}{\lambda}$$

→ 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,
θn = $$\frac{nλ}{a}$$

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