Answer the following question.
Define the term, "refractive index" of a medium. Verify Snell's law of refraction when a plane wavefront is propagating from a denser to a rarer medium.
Refractive index of a medium may be defined as the ratio of the speed of light in air and the speed of light in the given medium. It doesn’t have a unit.
Refraction On The Basis Of Wave Theory
Consider any point Q on the incident wavefront.
Suppose when disturbance from point P on incident wavefront reaches point P' on the refracted wavefront, the disturbance from point Q reaches Q' on the refracting surface XY.
Since P'A' represents the refracted wavefront, the time taken by light to travel from a point on incident wavefront to the corresponding point on the refracted wavefront should always be the same. Now, the time taken by light to go from Q to Q' will be
`t = "QK"/c + "KQ'"/"v"` ....(i)
In right-angled ΔAQK,
∠QAK = i
∴ QK = AK sin i … (ii)
In right-angled ΔP'Q'K,
∠Q'P'K = r
KQ' = KP' sin r ...(iii)
Substituting (ii) and (iii) in equation (i),
`t = ("AK"sin i)/(c) + ("KP"'sin r)/("v")`
Or, `t = ("AK"sin i)/(c) + (("AP'"- "AK")sin r)/v ....(∵ "KP"' = "AP"' - "AK")`
Or, `t = ("AP"')/(c) sin r + "AK" (sin i/c - sin r /"v")` ....(iv)
The rays from different points on the incident wavefront will take the same time to reach the corresponding points on the refracted wavefront i.e., t given by equation (iv) is independent of AK. It will happen so, if
`sin"i"/c - sin"r"/"v"` = 0
`sin "i"/sin "r" = c / "v"`
However, `c/"v" = mu`
∴ `mu = sin"i"/sin"r"`
This is the Snell’s law for refraction of light.