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Wave Optics Class 12 Notes Physics Chapter 10

Huygens Principle:- Wave-front  of a wave, at any instant , is defined as the locus of all the particles in the medium which are being disturbed at the same instant of time and are in the same phase of vibration.
(a) Each point on a wave front acts as a source of new disturbance and emits its own set of spherical waves called secondary wavelets. The secondary wavelets travel in all directions with the velocity of light so long as they move in the same medium.
(b) The envelope or the locus of these wavelets in the forward direction gives the position of new wave front at any subsequent time.
Wave Optics Class 12 Notes Physics Chapter 10

  • Determination of Phase Difference:-
    The phase difference between two waves at a point will depend upon
    (a) The difference in path lengths of the two waves from their respective sources.
    (b) The refractive index of the medium
    (c) Initial phase difference between the source if any.
    (d) Reflections, if any, in the path followed  by waves.
  • Reflection of plane wave at plane surface (Laws of reflection):-
    (a) The incident ray, the reflected ray and normal to the reflecting surface at the point of incidence, all lie in one plane and that plane is perpendicular to the reflecting surface.
    (b) The angle of incidence is equal to the angle of reflection.
    So, ∠i = ∠r
    This signifies angle of incidence is equal to the angle of reflection.
    Wave Optics Class 12 Notes Physics Chapter 10
  • Refraction of light:-
    Refraction is the phenomena by virtue of which a wave going from one medium to another undergoes a change in velocity.
    (a) The sine of the angle between the incident ray and the normal bears a constant ratio to the sine of the angle between refracted ray and the normal.
    sin i/sin r = v1/v2 = 1µ= constant
    Here, v1 and v2 are the velocities of sound in first and second medium respectively.1µ2 is the refractive index of the second medium with respect to first.
    (b) The incident ray, the refracted ray and the normal to the refracting surface lie in the same plane.
    Wave Optics Class 12 Notes Physics Chapter 10
  • Interference:- The modification in the distribution of light energy obtained by the superposition of two or more waves is called interference.
  • Principle of superposition:- It states that a number of waves travelling, simultaneously, in a medium behave independent of each other and the net displacement of the particle, at any instant, is equal to the sum of the individual displacements due to all the waves.
  • Displacement equation:- y =  R sin 2π/λ (vt+x/2)
  • Amplitude:- R = 2a cos πx/λ
  • Intensity:- I = K4a2 cos2 (πx/λ)    [I = KR2]
  • Maxima:- A point having maximum intensity is called maxima.
    x = 2n (λ/2)
    A point will be a maxima if the two waves reaching there have a path difference of even multiple of λ/2.
    Imax = 4Ka2 = 4i   (Here, i = Ka2)
  • Minima:- A point having minimum intensity is called a minima.
    x = (2n+1) (λ/2)
    A point will be a minima if the two waves reaching there have a path difference of odd multiple of λ/2.
    Imin = K. 4a2×0 = 0
  • Condition for constructive interference:-
    Path difference = (2n)λ/2
    Phase difference = (2n)π
  • Condition for destructive interference:-
    Path difference = (2n+1)λ/2
    Phase difference = (2n+1)π
  • Coherent Sources:- Coherent sources are the sources  which either have no phase difference or have a constant difference of phase between them.
  • Conditions for interference:-
    (a) The two sources should emit, continuously, waves of same wavelength or frequency.
    (b) The amplitudes of the two waves should be either or nearly equal
    (c) The two sources should be narrow.
    (d) The sources should be close to each other.
    (e) The two sources should be coherent one.
  • Young’s double slit experiment:-
    Path difference, x = yd/D
    Maxima, y = nλD/d
    Here, n = 0,1,2,3….
    Minima, y = (2n+1) λD/d
    Here, n = 0,1,2,3….
  • Fringe Width:- It is the distance between two consecutive bright and dark fringes.
    β = λD/d
  • Displacement of fringes due to the introduction of a thin transparent medium:-
    (a) Shift for a particular order of fringes:-
    y = (β/λ) (µ-1)t
    (b) Shift across a particular point of observation:-
    µ = (mλ/t) +1
  • Lloyd’s single mirror:-
    λ = β .2a/D
  • Power of lens:- P = 100/f
  • Magnifying power or magnification of a simple microscope:- M= 1+(D/f)
  • Magnifying power or magnification of a compound microscope:-
    M= L/f0 (1+D/fe)
    Here, f0 is the focal length of the objective, fis the focal length of the eyepiece and L is the length of the microscope tube.
  • Magnification of astronomical telescope in normal adjustment:-
    M = f0/fe
  • Magnification of astronomical telescope, when the final image is formed at the distance of distinct vision:-
    M = (f0/fe) [(fe+D)/D]
  • Magnifying power M of Galileo’s telescope:-
    M = focal length of objective/focal length of eye lens = F/f
  • Diffraction:- Diffraction is the bending  or spreading of waves that encounter an object ( a barrier or an opening) in their path.
    (a) In Fresnel class of diffraction, the source and/or screen are at a finite distance from the aperture.
    (b) In Fraunhofer class of diffraction, the source and screen are at infinite distance from the diffracting aperture. Fraunhofer is a special case of Fresnel diffraction.
    Wave Optics Class 12 Notes Physics Chapter 10
    If Im represents the intensity at O, its value at P is
    Iθ = Im (sinα/α)2
    Here, α = ?/2 = πa sinθ/λ
    A minimum occurs when, sin α = 0 and α is not equal to zero.
    so  α = nπ,       n = 1, 2, 3...
    So, πa sinθ/λ = nπ
    Or, a sinθ = nλ
    Angular width of central maxima of diffraction pattern = 2θ1 = 2 sin-1(λ/a)
    [ θgives the angular position of first minima]
  • Polarization: - Polarization of two interfering wave must be same state of polarization or two source of light should be un polarized.
  • Brewster Law:-
    According to this law when un polarized light is incident at polarizing angle (i) on an interface separating a rarer medium from a denser medium, of refractive index m as shown in Fig., below such that,
    µ = tan i
    Then light reflected in the rarer medium is completely polarized. Reflected and refractive rays are perpendicular to each other.
    Wave Optics Class 12 Notes Physics Chapter 10
  • Reduction in Intensity:- Intensity of polarized light is 50% of that of the un polarized light, i.e.,
    Ip = Iu/2
    Here, Ip = Intensity of polarized light.
    Iu = Intensity of un polarized light.
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FAQs on Wave Optics Class 12 Notes Physics Chapter 10

1. What is wave optics?
Ans. Wave optics is a branch of physics that deals with the study of light as a wave phenomenon. It focuses on the behavior of light waves, including phenomena such as diffraction, interference, polarization, and the wave nature of light.
2. What is the difference between wave optics and geometric optics?
Ans. Wave optics and geometric optics are two different approaches to studying light. Geometric optics describes light as rays and focuses on the propagation of light in straight lines, considering phenomena like reflection and refraction. Wave optics, on the other hand, treats light as a wave and considers its interactions with other waves and matter.
3. What is interference in wave optics?
Ans. Interference in wave optics refers to the interaction of two or more light waves that results in either reinforcement (constructive interference) or cancellation (destructive interference) of the waves. It leads to the formation of interference patterns, such as bright and dark fringes, which are observed in phenomena like the double-slit experiment.
4. How does diffraction occur in wave optics?
Ans. Diffraction in wave optics is the bending or spreading out of light waves as they pass through an aperture or encounter an obstacle. It occurs due to the wave nature of light, where the waves spread out and interfere with each other, resulting in a pattern of alternating bright and dark regions. Diffraction is responsible for phenomena like the spreading of light around corners and the formation of patterns in single-slit and multi-slit experiments.
5. What is polarization in wave optics?
Ans. Polarization in wave optics refers to the orientation of the electric field vector of light waves. It describes the direction in which the electric field oscillates. Polarized light waves have their electric field vectors aligned in a specific direction. Understanding polarization is crucial for various applications, such as 3D glasses, optical filters, and liquid crystal displays (LCDs).
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