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.

: Rarer medium to denser medium:-__Case 1__

- The waves generated in medium 1 will have velocity as v
_{1}τ. - Waves in denser medium will have lesser velocity as compared to velocity in rarer medium.It is given as v
_{2}τ. - 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) =(v
_{1}τ) /(v_{2}τ) - => (sin i/sin r) =(v
_{1}/v_{2}) - 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/n
_{1})/(c/n_{2})- Where n
_{1}and n_{2 }are the refractive index in medium 1 and 2 resp.

- Where n
- Snell’s law (
**sin i/sin r) = (n**Hence proved._{1}/ n_{2}). __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.
- => v
_{1}> v_{2}- Where v
_{1}= velocity in denser medium and v_{2}=velocity in rarer medium.

- Where v
__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.
- =>v
_{1}< v_{2} - 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.v
_{1}< v_{2}. - => 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) =(v
_{1}τ) /(v_{2}τ) - => (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/n
_{1})/(c/n_{2})- Where n
_{1}and n_{2 }are the refractive index in medium 1 and 2 resp.

- Where n
- Snell’s law (
**sin i/sin r) = (n**Hence proved_{1}/ n_{2}).**.** - Angle of incidence is less than angle of refraction, i<r.
- => v
_{1}< v_{2}. - Special case: - If i = i
_{C}=> r = 90^{0}. In this case there will be no refraction and__total internal reflection__takes place.- Where i
_{C}= critical angle.

- Where i

.