Solveeit Logo

Question

Question: The critical angle of glycerine-air is \(43^\circ \). Find the refractive index of glycerine \((\sin...

The critical angle of glycerine-air is 4343^\circ . Find the refractive index of glycerine (sin43=0.68)(\sin 43^\circ = 0.68)

Explanation

Solution

The critical angle of a medium is the angle such that if the incident angle of a ray of light going from a denser to a rarer medium is greater than the critical angle, the ray of light will be reflected back in the medium. It depends on the refractive index of the denser medium and can be determined from Snell’s law.
Formula used: In this solution, we will use the following formula:
Snell’s law μ1sinθ1=μ2sinθ2{\mu _1}\sin {\theta _1} = {\mu _2}\sin {\theta _2} where μ1{\mu _1} is the refractive index of the first medium and μ2{\mu _2} , the second. θ1{\theta _1} and θ2{\theta _2} are the incident and the refractive index of the ray of light.

Complete step by step answer:
We’ve been given the critical angle of the glycerine-air medium as 4343^\circ . Let us start by finding the formula of critical angle from Snell’s law:
For the critical angle, the ray of light will be completely perpendicular to the normal. So, θ2=90{\theta _2} = 90^\circ . As the second medium is air, so μ2=1{\mu _2} = 1, we can write
sinθ1=1μ1\sin {\theta _1} = \dfrac{1}{{{\mu _1}}}
Or
θ=sin1(1μ1)\theta = {\sin ^{ - 1}}\left( {\dfrac{1}{{{\mu _1}}}} \right)
μ1=1sinθ1\Rightarrow {\mu _1} = \dfrac{1}{{\sin {\theta _1}}}
Since the critical angle for the glycerine-air medium as 4343^\circ , we can find the refractive index of the glycerine as
μ1=1sin43=10.68{\mu _1} = \dfrac{1}{{\sin 43^\circ }} = \dfrac{1}{{0.68}}
Which gives us
μ1=1.47{\mu _1} = 1.47

Hence the refractive index of glycerine is μ1=1.47{\mu _1} = 1.47

Note: The critical angle is only defined for a transfer from a denser to a rare medium. In this case, glycerine is the denser medium and air is the rare medium. The critical angle will depend only on the refractive of the denser medium if the rarer medium is air as we can consider the refractive index of air to be 1.