A lightray incident at grazing angle at O ( angle of incidence 90o ) and refracted into a medium
of variable refractive index .
Let the light ray incident at a point A which is at y = 1 m with incident angle Φ .
Tangent at A makes angle Φ with normal as shown in figure .
when light ray is subjected to refraction due to refractive indices of incident and refracted medium,
we have product of absolute refractive index and sine of angle of incidence is constant ( snell's law of refraction )
Hence we have , μa sin(90) = μ sinΦ = μ sin(90-θ) = μ cosθ
where μa = 1 is refractive index of air
Hence from above expression, we get , μ cosθ = 1
slope m at point A is given as , m = tanθ = dy/dx = 4x = 4 × 1.0 = 4
if tanθ = 4 , then cosθ = 1 /
Hence from eqn.(1) , we get , μ = 1 / cosθ = = 4.12