Chapter : 10

What are Wave Optics ?

Term

Wavefronts

Definition / Explanation

  • The locus of all the particles which are vibrating in the same phase at any instant  is called wavefront.

Wavefronts

Spherical Wavefront (Point source)

Cylindrical Wavefront (thin rod source)

Plane Wavefront (Parallel beam of light)

  • A wave front always lies normal to the direction of propagation of waves i.e., normal to the rays of light.

Huygen’s Principle

  • Huygen principle states that every point on the given primary wavefront acts as a source of secondary wavelets, sending out disturbance in all directions in a similar manner as the original source of light does.
  • The new position of the wavefront at any instant called secondary wavefront is the envelope of the secondary wave lets at that instant.
  • The secondary wavelets have same frequency, wavelength as original waves but has reduced intensity.
  • Using Huygen’s principle, law of reflection and refraction can be proved on the basis of wave theory.

Interference of light

  • The phenomenon of redistribution of energy as a result of superposition of light waves from two coherent sources is called intereference of light.
  • Where resultant intensity is maximum interference said to be constructive and where the resultant intensity is minimum interference is said to be destructive.

Thomas Young’s Double Slit Experiment

  • Young’s double slit experiment was the first to demonstrate the phenomenon of interference of light. Using two slits illuminated by a monochromatic light source,
    an interference pattern is obtained on the screen. This interference pattern of
    alternate bright and dark bands of equal width, known as interference fringes. All
    the bright fringes have same intensity and all the dark fringes are perfectly dark.
  • For constructive interference (Formation of bright fringes)

Path difference = xn(d/D)=nλ

Where n = 0 for central bright fringe

n = 1 for first bright fringe

n = 2 for second dark fringe and so on

d = distance between slits

D = distance between slits and screen

xn = distance of nth bright fringe from the centre.
  • For destructive interference (Formation of dark fringes)
Path difference = xn(d/D)=(2n-1)(λ/2)
Term
Definition / Explanation

Where n = 1 for first dark fringe,

n = 2 for second dark fringe and so on.

xn = distance of nth dark fringe from the centre

The width of each bright dark interference fringes is found to be,

β=(λD/d)

where λ is the wavelength of light.

Coherent Source

Coherent source are those which emits continuous light waves of same amplitude, same wavelength/frequency in same phase or having constant phase difference. Two independent source can never be coherent sources are an essential requirement of interference of light.

Single Slit Diffraction / Diffraction of Light

The diffraction pattern produced by a single slit consists of a central weak band with alternating bright and dark bands of decreasing intensity on both sides xCondition for nth secondary minimum is that path difference

a sin θ = mλ

where m = 1, 2, 3, ............

Condition for nth secondary maximum, is that path difference

a sin θ = (2m + 1)(λ/2)

where m = 1, 2, 3, .........

  • Width of central maximum = 2x =(2λD/a)=(2fλ/a)
  • Where, a = slit width

D = slit and screen distance

f = focal length waves

Polarization

  • Phenomenon of restricting the vibration of light (electric vector) in a particular direction, on passing ordinary unpolarized light through certain crystal like tourmaline crystal the plane in which vibration of polarized light are confined is called plane of vibration, and a plane perpendicular to the plane of vibration is called plane of polarization.
  • On rotating the crystal about the direction of propagation as axis, intensity of plarized light does not change on the contrary, when polarised light is passed
    through another crystal called analyser and the analyser is rotated, the transmitted fraction of light changes from maximum to zero.