Laws of refraction
1. Incident ray, refracted ray and the normal all lie in one plane.
2. Ratio of sine of angle of incidence to the sine of angle of refraction is constant.
\(\frac{sin\ i}{sin\ r} \) = constant = 1µ2
This constant denoted by is called refractive index of medium 2 (in which refracted ray lies) w.r.t. medium 1 (in which incident ray lies).
This law is also called Snell's law.
Let us consider refraction of light as a plane beam of light passing from air to water. Fig.
The incident rays AB, EF make an angle i at B, F with the normal to the plane separating air and water. The refracted rays BC and FG are at angle r with respect to the normal, r is the angle of refraction. BH is normal to EF and FJ normal to BC. Note that the incident ray, the refracted ray and the normal to the plane at the point of incidence lie in the same plane. The phase of the plane light wavefront is the same all along BH (in air) as also along the refracted waterfront JF (in water). Therefore, by the time the ray HF travels in air, the corresponding ray BJ travels in water.
∠HBF = i and ∠BFJ = r
In ∆ HBF, sin i = \(\frac{HF}{BF}\)
In ∆ BFJ, sin r = \(\frac{BJ}{BF}\)
Therefore, \(\frac{sin\ i}{sin\ r} = \frac{HF}{BF} = \frac{v_1}{v_2t}\) = 1µ2
where \(\frac{v_1}{v_2}\) = 1µ2 the refractive index of water with respect to air.
