Prove laws of reflection using Huygens' principal.
(OR) Proof for laws of reflection using Huygens' Principal:

Explanation

(i) Consider a beam of white light passes through a prism, it gets dispersed into its constituent colours. (ii) Let` delta_V , delta_R` are the angles of deviation for violet and red light. Let n, and n, are the refractive indices for the violet and red light respectively. (iii) The refractive index of the material of a prism is given by the equation,
` n = (sin ((A+D)/(2)))/(sin (A/2))`
(iv) Here A is the angle of the prism and D is the angle of minimum deviation. If the angle of prism is small of the order of `10^@` , the prism is said to be a small angle prism. (v) When rays of light pass through such prisms, the angle of deviation also becomes small. If A be the angle of a small angle prism and `delta` the angle of deviation then the prism formula becomes.
` n = (sin ((A+ delta)/(2)))/(sin (A/2))`
For small angles of A and ` delta_m`
` sin ((A+delta)/(2)) ~~ ((A+delta)/(2))`
` sin (A/2) ~~(A/2)`
` therefore n = ((A+delta)/(2))/(A/2) = (A + delta)/(A) = 1 + delta/A`
Further simplifying , ` delta/A = n - 1 `
` delta = (n - 1) A`
(vi) When white light enters the prism, the deviation is different for different colours. Thus, the refractive index is also different for different colours.
For Violet light, `delta_V = (n_V - 1) A`
For Red light, `delta_R = (n_R - 1) A`
(vii) As, angle of deviation for violet colour `delta_V` is greater than angle of deviation for red colour `delta_R` the refractive index for violet colour `n_V` is greater than the refractive index for red colour `n_R`
Subtracting `delta_V` from `delta_R` we get,
`delta_V - delta_R = (n_V - n_R) A`
(viii) The term (`delta_V - delta_R`) is the angular separation between the two extreme colours (violet and red) in the spectrum is called the angular dispersion.