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 × 10^{14} Hz) and minimum for red colour (4.3 × 10^{14} 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 = I_{0} cos^{2} 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 = \(\frac{\mathrm{I}_{\mathrm{i}}}{2}\) cos^{2} 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 I_{0} = \(\frac{\mathrm{I}_{\mathrm{i}}}{2}\)

→ 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

n_{1}λ_{1} = n_{2}λ_{2}

→ 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,

θ_{1} = \(\frac{λ}{a}\)

→ 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.