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CBSE NOTES CLASS 12 PHYSICS

CHAPTER 10 WAVE OPTICS

Newton’s corpuscular theory

Wave theory - nature of electromagnetic waves

Wave front

Huygens principle

Refraction of a plane wave from rarer to denser medium

Refraction of a plane wave from denser to rarer medium

Reflection of a plane wave by a plane surface

Behaviour of a plane wave front with different surfaces

The Doppler effect

Superposition principle

Coherent sources of light

Interference of light

Young’s double slit experiment

Fringe width in double slit experiment

Diffraction of light

Single slit experiment

Double slit vs single slit patterns

Interference vs diffraction due to single slit

Constraints for diffraction due to single slit

Viewing the diffraction pattern

Energy is conserved during interference and diffraction

When can we consider the light beam to be parallel beam in single slit experiment?

Resolving power of an objective lens

Fresnel distance

Polarisation

Polarisation by transmission

Polarisation by scattering

Polarisation by reflection - Brewster’s law

Law of Malus

Polaroid and uses of polaroids

CBSE NOTES CLASS 12 PHYSICS

CHAPTER 10 WAVE OPTICS

Interference

Superposition of two waves, travelling through the same medium, is called interference.

Constructive interference occurs when the two interfering waves have a displacement in the same direction and the amplitude of the resulting wave is the addition of amplitudes of interfering waves.

Destructive interference occurs when the two interfering waves have a displacement in different direction (out of phase) and the amplitude of the resulting wave is the difference of amplitudes of interfering waves.

???

Consider two coherent sources S1 and S2 a point P for which S1P = S2P. Since the distances S1P and S2P are equal, waves from S1 and S2 will take the same time to travel to the point P and waves that originate from S1 and S2 in phase will also arrive, at the point P, in phase.

???

If the displacement produced by the source S1 at the point P is given by

y1 = a cos ωt

then, the displacement produced by the source S2 (at the point P) will also be given by

y2 = a cos ωt

Thus, the resultant of displacement at P would be given by

y = y1 + y2 = 2 a cos ωt

Since the intensity is the proportional to the square of the amplitude, the resultant intensity will be given by,

I = 4Io

where Io represents the intensity produced by each one of the individual sources; Io is proportional to a2.

In fact for all points where the phase difference is 2nπ or path difference is nλ, the interference will be constructive.

???

If the phase difference is (2n+1)π or path difference is 2n+12λ, the interference will be destructive.

???

For any other arbitrary point let the phase difference between the two displacements be φ.

y1 = a cos ωt ⇒ y2 = a cos (ωt + φ)

The resultant displacement will be given by

y = y1 + y2 = a [cos ωt + cos (ωt + φ]

= 2acosφ2cosωt +φ2

Since φ is constant, the amplitude of the resultant displacement is 2a cos φ2.

Or the intensity I = 4Io cos2 φ2

If the two sources are not coherent the average intensity will be given by

<I> = 4Io <cos2 φ2>

where angular brackets represent time averaging.

The function cos2 φ2 will randomly vary between 0 and 1 and the average value will be 12.

The resultant intensity will be given by,

I = 2Io

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