(i) Consider a parallel beam of light is incident on a refracting plane surface XY such as a glass surface as shown in Figure.
(ii) The incident wavefront AB is in rarer medium (1) and the refracted wavefront A'B' is in denser medium (2). (iii) These wavefronts are perpendicular to the incident rays L, M and refracted rays L',M' respectively. (iv) By the time the point A of the incident wavefront touches the refracting surface, the point B is yet to travel a distance BB' to touch the refracting surface at B. (v) When the point B falls on the refracting surface at B', the point A would have reached A' in the other medium. This is applicable to all the points on the wavefront. Thus, the refracted wavefront AB emanates as a plane wavefront. (vi) The two normals N and N' are considered at the points where the rays L and M fall on the refracting surface. (vii) As refraction happens from rarer medium (1) to denser medium (2), the speed of light is `v_1` and `v_2` before and after refraction and `v_1` is greater than `v_2 (v_1 gt v_2)`. But, the time taken t for the ray to travel from B to B' is the same as the time taken for the ray to travel from A to A'
` t = (BB')/(v_1) = ("AA"')/(v_2) " or " (BB')/("AA"') = v_1/v_2`
(i) The incident rays, the refracted rays and the normal are in the same plane.
(ii) Angle of incidence,
`i= angleNAL = 90^@ - angleNAB = angle BAB'`
Angle of refraction,
` r = angleN'B'M' = 90^@ - angleN'B'A' = angleA'B'A`
For the two right angle triangles `Delta`ABB' and `Delta`B' A' A,
`(sin i)/(sin r) = ((BB')/(AB'))/(("AA"')/(AB')) = (BB')/("AA"') = v_1/v_2 = ((c)/(v_2))/((c)/(v_1))`
(viii) Here, c is speed of light in vacuum. Theratio `c/v` is the constant, called refractive index of the medium. The refractive index of medium (1).is, `(c)/(v_1) = n_1` and that of medium (2) is, `(c)/(v_2) = n_2`
` (sin i)/(sin r) = (n_2)/(n_1)`
In product form,
`n_1 sin i = n_2 sin r `
Hence, the laws of refraction are proved.
(ix) In the laws of refraction can also be proved for wavefront travelling from denser to rarer medium. (x) Light travels with greater speed in rarer medium and lesser speed in denser medium. Hence, the wavelength of the light is longer in rarer medium and shorter in denser medium.
`(lamda_1)/(lamda_2) = n_2/n_1`
