Class 12 Physics Wave Optics Refraction of plane waves

Refraction of plane waves

  • In refraction, when any point of the incident wavefront interacts with boundary, secondary waves are generated and they will have some velocity.
  • Case 1: Rarer medium to denser medium:-
  • The waves generated in medium 1 will have velocity as v1τ.
  • Waves in denser medium will have lesser velocity as compared to velocity in rarer medium.It is given as v2τ.
  • The wavefront will not be a circle as the waves in two different mediums are travelling with different velocities.
  • To prove Snell’s law:-
    • Consider two triangle’s ABC and AEC :-
    • In triangle ABC sin i= (BC/AC) and sin r=(AE/AC)
    •  By dividing (sin i/sin r) = (BC/AC) x (AC/AE)
    • Therefore (sin i/sin r) = (BC/AE) =(v1τ) /(v2τ)
    • => (sin i/sin r) =(v1/v2)
    • Refractive index n; =(c/V) 
      • Where c = velocity of light in vacuum and V=velocity of light in medium.
  • Therefore (sin i/sin r) = (c/n1)/(c/n2)
    • Where n1 and n2 are the refractive index in medium 1 and 2 resp.
  • Snell’s law (sin i/sin r) = (n1/ n2). Hence proved.
  • Case 1: Angle of incidence is greater than angle of refraction, i>r
    • Light rays bend towards the normal when it travels from rarer medium to denser medium.
    • => v1> v2
      • Where v1 = velocity in denser medium and v2 =velocity in rarer medium.
    • Case 2: Angle of incidence is less than angle of refraction, i<r.
    • Light rays bend away from the normal when it travels from denser medium to rarer medium.
    • =>v1< v2
    • Conclusion: Velocity in rarer medium > Velocity in denser medium.
    • This is contrary to Newton’s theory.
    • Huygens theory was able to prove all the laws of refraction. That is why his theory was accepted.
    • Case 2:- Denser medium to rarer medium.
      • In refraction any point of the incident wavefront interacts with boundary, secondary waves will be formed and these secondary waves will have some velocity.
      • Velocity in denser medium is lesser than the velocity in the rarer medium, i.e.v1< v2.
      • => Radius of wavefronts in rarer medium < Radiusof wavefronts in denser medium.
  • To prove Snell’s law:-
    • Consider two triangle’s ABC and AEC :-
    • In triangle ABC sin i= (BC/AC) and sin r=(AE/AC)
    •  By dividing (sin i/sin r) = (BC/AC) x (AC/AE)
    • Therefore (sin i/sin r) = (BC/AE) =(v1τ) /(v2τ)
    • => (sin i/sin r) =τ.
    • Refractive index n; =(c/V) 
      • Where c = velocity of light in vacuum and V=velocity of light in medium.
  • Therefore (sin i/sin r) = (c/n1)/(c/n2)
    • Where n1 and n2 are the refractive index in medium 1 and 2 resp.
  • Snell’s law (sin i/sin r) = (n1/ n2). Hence proved.
  • Angle of incidence is less than angle of refraction, i<r.
  • => v1< v2.
  • Special case: - If i = iC => r = 900 . In this case there will be no refraction and total internal reflection takes place.
    • Where iC= critical angle.

Share these Notes with your friends  

< Prev Next >

You can check our 5-step learning process


.