RBSE Class 12 Physics Notes Chapter 10 Wave Optics

These comprehensive RBSE Class 12 Physics Notes Chapter 10 Wave Optics will give a brief overview of all the concepts.

RBSE Class 12 Physics Chapter 10 Notes Wave Optics

Huygens’ Principle and Interference:
Huygens’ principle is a geometrical construction used to find the new position of a wavefront at a later time from its given position at any instant. It states that :

• All the particles on a wavefront called primary wavefront can be regarded as point sources of new disturbance called the secondary wavelets which travel out with the same velocity as that of the original waves, provided the medium is the same.
• A surface tangential to the secondary wavelets gives the position and shape of the new wavefront.

Wavefront:
Wavefront is the continuous locus of all the particles of a medium, which are vibrating in the same phase superposition principle states that when a number of waves travelling simultaneously in the same medium overlap one another (superimpose), then the resultant displacement at any instant at any point in space is equal to the vector sum of the instantaneous displacements of individual waves.

The resultant displacement \(\vec{y}\) will be
\(\vec{y}=\vec{y}_1+\vec{y}_2+\ldots \ldots \ldots+\vec{y}_n\)

Coherent sources:
Two sources are said to be coherent, if they emit light waves of the same frequency or wavelength and a constant phase difference (or no phase difference).

Conditions for obtaining two coherent sources of light

• Coherent sources of light should be obtained from a single source.
• Two sources should give monochromatic light.
• The path difference between two light waves from the two sources should be small

Interference of light:
Interference of light is the phenomenon of redistribution of light energy due to superposition of waves from two coherent sources of light.

Sustained interference:
Sustained interference is the interference in which the position of. maxima and minima of light remains fixed all along the screen.

• For constructive interference
  Path difference - n λ
• For destructive interference
  Path difference = (2n - 1)\(\frac{\lambda}{2}\)
• Fringe width β in interference of light is given by
  β = \(\frac{\lambda \mathrm{D}}{d}\)
• And all bright and dark fringes are of the same width.

Ratio of intensity of light at maxima and minima is given by
\(\frac{I_{\max }}{I_{\min }}=\frac{\left(a_1+a_2\right)^2}{\left(a_1-a_2\right)^2}\)
where a₁ and a₂ are the amplitudes of two interfering light waves.

Ratio of intensities of light due to two sources:
If w₁ and w₂ are widths of two slits and I₁ and I₂ are intensities of light due to respective slits, then
\(\frac{w_1}{w_2}=\frac{I_1}{I_2}\) ............(i)
Also,
\(\frac{\mathrm{I}_1}{\mathrm{I}_2}=\frac{a_1^2}{a_2^2}\)
∴ \(\frac{w_1}{w_2}=\frac{a_1^2}{a_2^2}\) ...........(ii)

Diffraction And Polarisation:
Diffraction is the phenomenon of bending of light around corners of an obstacle or aperture and spreading into the regions of the geometrical shadow.

Diffraction is of two types

• Fresnel diffraction: In this type of diffraction, the source of light and the screen have at finite distance from the slit and hence the wavefront spherical or cylindrical.
• Fraunhofer diffraction: In this type of diffraction, the source and screen are at infinite distance from the slit and thus the wavefront is plane.

Slit:
It is a rectangular opening whose width is very small as compared to its length.

Diffraction at a single slit:
For nth secondary maximum
Path difference = a sin θ_n = (2n + 1)\(\frac{\lambda}{2}\)

For nth secondary minimum
Path difference = a sin θ_n = nλ
Width of secondary maxima (or minima)
β = \(\frac{\lambda \mathrm{D}}{a}\)

Width of central maxima = 2β = \(\frac{2\lambda \mathrm{D}}{a}\)

Resolving power:
Resolving power of an optical instrument is its ability to resolve or to see as separate, the images of two closely spaced objects.
Resolving power of microscope
d = \(\frac{\lambda}{2 \mu \sin \theta}\)

Resolving power of telescope = \(\frac{a}{1.22 \lambda}\)

Polarisation:
Polarisation is the phenomenon of restricting the waves in oscillations to particular plane is called polarisation. When all the oscillations get confined along one direction, the wave is called plane polarised.

Nicol prism:
Nicol prism is an optical device used for producing and analysing plane polarised light.

Malus law:
It states that the intensity of polarised light transmitted through the analyser varies as square of cosine of the angle between the plane of transmission of analyser and polariser
i.e. I ∝ cos²θ

Brewster’s law:
It states that when light is incident at the polarising angle, the reflected and refracted rays are perpendicular to each other.
Or
When light is incident at polarising angle at the interface of a refracting medium, the tangent of the polarising angle is equal to the refractive index of the medium.
i.e. μ = tan i_p

Polaroids:
Polaroids are artificially made large sheets or plates capable of producing a strong beam of polarised light.

Uses:
Polaroids are used in :

• three dimensional motion pictures
• taking clear photographs of white clouds
• wind shields of automobiles
• in window panes of trains and aeroplanes
• in sun glasses;