A typical prism is a solid figure, a transparent homogenous and isotropic medium bounded by 2 non-parallel plane surfaces ( each forms a parm ). In geometrical optics, we can view a prism as a triangle characterized by its vertex angle alpha ( suppose 'a' ) and its index of refraction n. A prism can be used to cause dispersion of a beam of white light dividing it into its respective components , each of its own wavelength or frequency.
Suppose a ray of light propogating through air hits one face of an isosceles prism , the emergent ray is deviated towards the base of the prism relative to the incident ray. The angle of deviation is that between the 1st incident ray and 2nd refracted ray , designated ?d.
1-Assuming the 2nd angle of incidence ?i2 ? ?critical, and that Sin ( ? ) ? ? ( in radians ) for small angles, prove that for small incident angles & a small angle alpha 'a' ( of the prism ), ?d = a ( n - 1 ) i.e. independent of ?i2
2-Incase of minimum deviation, find the expression of n in terms of ?m ( minimum angle of deviation ) and alpha 'a'. Deduce, incase of small angles , n = ( ?m + a ) / a
Only basic algebra + trigonometry involved ... happy hunting Xiankai.