✤ WAVE FRONT :- When light travel in a medium then particle of the medium vibrate continuously in same phase this continuous locus of particle is called                               wave front.

                        

                  § Nature of wave front depend upon the shape and size of source of light.

                      Ex -> Plane Spherical Cylindrical Wavefront Wavefront

                      Ex.

                             1. Light diverging from a Point source → spherical.

                             2. Light emerging out from a convention → Plane wavefront

                             3. Light coming from a distant star → Plane w.f.

 ✤ HUYGEN'S Principle: It is based on wave theory of light.

                   (i) Every Particle in a wave front act as a new source of light for next Particle.

                   (ii) Tangent is drawn in forward direction of vibrating particles act as SWF and in backward direction act as PWF. R.

                         The amplitude of wavelet is max in forward direction and zero in backward direction.

                                Amplitude wavelet = 1+cos θ

                                             forward θ = 0°

                                          backward θ = 180°

                                                     1+cos 180°/2

                                                    1+ (-1) = 20

✤ Application of Huygens's

          1.    Proof of law & reflection.

                                

                 Let AB is on incident wavefront consists 3 rays (1,2,3) let speed of light = C,

                             So CA' = C X t

                 Make an arc A'B' = c x t, i.e. A’B’ is Reflected waves front.

                Now in ABA' and A'B'A

                              BA’ = AB’ (Cxt)

                              AA’ = Common

                :. By RHS, ABA’ and A’B’A are congruent

                            By CPCT I = r

  2. Proof of law of Refraction:

                    ( from rarer to denser )

                       In ABA’ sin I = BA’ / AA’

                       In A’B’A sin r= AB’ / AA’

                       Sin i / Sin r = BA’ / AB’

                           = c1 X t1/ c2 X t2

                       Sin I / Sin r = c1 / c2

                       Sind' = M

                       which is the law of refraction.

  ✤ Principle of superposition:

              Let y1 and y2 are two waves then after superimpose of y1 & y2

            New wave is formed

                         y = y1 + y2

✤ INTERFERENCE: It is defined as the phenomena of redistribution of light energy.

                                                    INTERFERENCE    

        Intensity of light is maximum              Intensity of light is minimum dark

✤ Conditions for constructive interference:

             we know Amplitude of resultant wave

                  R = √(a² +b² + 2ab cos φ) 

             Here a and b are amplitude of interference wave.

                    φ = Phase difference b/w two waves.

             for constructive  Intensity is maximum for which R should be maximum.

                   i.e cos φ = max

                         cos φ = 1

                            ⇒ φ = 2nπ

                    we know path diff = λ /2π x φ

                             x = λ/2π x 2nπ

                             x = nλ

                Resultant amplitude Rmax = a + b and Intensity Imax α R²max

                          ⇒ Imax α (a+b)²

✤ Conditions for destructive => for destructive Intensity of light should be minimum (zero) for which R should be minimum for which cos φ = minimum

                                cos φ = -1

                            ⇒ φ = (2n-1)π

                  we know path diff x = λ/2π x φ

                             x = λ/2π (2n-1)π

                             x = (2n-1) λ / 2

                  Resultant amplitude

                         Rmin = a-b

               and intensity minimum

                         Imin α R²min

                         Imin α (a-b)²

              Note:

                    1) Imax / Imin = (a+b)² / (a-b)²

                    2) I1 / I2 = a2 / b2 Here a, b are amplitude.

                    3) I₁ / I2 = w₁ / w2 w1, w2 are width.

✤ Types of source of light:

               1)  Coherent                2) Incoherent

    If two source of light. emit the If two sources do not emit the light of light of Same freq. (or same frequency and do not have zero wavelength) with zero     or phase difference then they are called Constant phase difference are Incoherent known as coherent

            Note:      1. two source should obtained from single source

                           2. two source emit the light of monochromatre.

            Note:     two independent source can't be coherent.

❈ Sustained interference: In this interference Position of minimum and minima of intensity on the screen do not change with time.

            Conditions:-  1. The sources (two) should continuously emit wave of same frequency or wave length.

                                 2. Two source should be coherent.

                                 3. for better contrast, amplitude of two wave should be equal.

                                 4. Interferencing wave should be in the same state of polarisation.

✤ Intensity distribution curve

        Note: in interference energy always remain conserved.

❋ Young's double slit experiment (Y.D.SE): → It is the practical explanation of interference.

                     Let two wave interference at P point. distance of P from centre is x and width of slit = d.

                        then the Position of bright fringe                 x = n λD / d

                

                Note: When A&B are ∞ close i.e. dis. small the position of fringe (x) uv large-hence a single fringe may occupy the whole screen: no interference                             pattern detected.

                         When A&B are far away (ov will be v small the interference pattern cannot be detected.)

❋ Width of fringe: It is the difference b/w two successive dark or two successive bright fringes distance from the centre.

        :. ß = Xn - Xn-1

         β = λD / d

      Note: width of dark and bright fringes always equal.

                1. angular width θ = λ/a

                2. If refractive index of medium is μ then width β’ = β/μ

                3. Angular Position of nᵗʰ bright fringe.

                              θₙ = xₙ/D

                             θ = nλ/d

✤ Some Imp Questions

           1. Why are coherent sources necessary to obtain a sustain interference.

2. What happen to interference if the phase difference b/w two sources varies continuously.

3. When a thin transparent film is placed just in front of one of its slit in YDSE using white light, what change results in the fringe system.

4. What changes in the interference pattern in YDSE will observed when

          1) light of smaller frequency is used.

          2) apparatus is immersed in water.

5. One of the two slit in YDSE is so painted that it transmit half Intensity, what is the effect on interference.

✤ Diffraction of light : It is the phenomenon by which light bends in the shadow of a sharp object like blade.

                    Note: diffraction pattern depend upon the comparison b/w amplitude or wavelength and slit width (a).

                                                        

❆ Fresnel distance: It is the maximum distance travel by the light before bending in the shadow of sharp object.

                                                    Zf = a²/λ

    

Note: Ray optics is valid upto a distance of 4000cm or 40m from the aperture.

                AB = width of the slit = a

        Let initally diffraction does not take place, o is the position of central maxima.

        Let angle of diffraction is o and P is the Position of interference.

                            Path dif (BM) = a.sinθ

                  for constructive Poth diff = (2n+1) λ /2

                         asin θ = (2n+1) λ/2

                for small angle Qn = (2n+1) λ / 2a

                        for destructive interference:

                Path diff = n λ

                         ⇒ asin θ = nλ

                 for small angle

                          θ = n λ / d

✤ Variation of intensity

        Note:  1. ‘0’ is called central maxima (maximum bright)

                   2. Position of nth secondary maxima

                           a sinθn = (2n+1)λ/2, n=1,2,3…

                   3. Direction of secondary maxima

                           θn = (2n+1)λ/2a;

                   4. minima position:

                            Qn = ± λ x n/a, n ≠ 0

                   5. distance of nth secondary maxima from centre.

                            Xn = (2n+1)λD/2a

         [[[[ the intensity of 2 maxima are with the n. With the increase in n (order of spectrum) then wavelets from lesser and lesser parts of the slit produce                 constructive interference to form 2nd maxima ]]]]]

                   6. with of central maximum

                         = 2β = 2 λ D /d

❆ difference b/w interference and diffraction:

             1. bright and dark                          1. They are difference in width.

                 fringes are of equal width

             2. All bright fringes are of              2. Intensity decreases with the distance

                 equal intensity from center.

             3. There is a perfect contrast         3. There is no proper contrast b/w

                  b/w bright and dark fringes.              them.

✤ Resolving Power of microscope:

              R.P = 2μsinθ / λ

                  μ = Refractive index of medium

                          λ= wave length of light used

✤ Resolving Power of telescope

                  R.P. = D / 1.22λ

                      D = diameter of objective lens

                      λ = wave length of light used.

Q. In YDSE, the intensity of light at a point on the screen where path difference is λ is k units. find the intensity at a point where path difference is

                (i) λ/4             (ii) λ/3

Ans:          we know I = I₁ + I₂ + 2√(I₁I₂) ̅ Cosφ, let I₁ = I₂ = I₀

                       I = I₀ + I₀ + 2I₀I₀ Cosπ/2

                            I = 2I₀ I₀ = I/2

                                I₀ = K/2

              (ii) your self.

Q. Two coherent sources of light of intensity ratio β. Prove that Imax - Imin / Imax + Imin = 2√β/ 1+β

Q. Why is no interference pattern observed when two coherent sources are

             (i) infinite close each other.

               (ii) far from each other.

Q. What changes in the interference Pattern in YDSE will be observed when

                 1) light of smaller frequency is used

                 2) the apparatus is immersed in water.

Q. What change will occur in diffraction Pattern If

                 1) light of smaller wave length is used.

                 2) slit is made narrower

                 3) frequency is changed.