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.  .