Refractive index of carbon disulphide for red light is 1.634 and the difference in the values of critical angle for red and blue light at the surface of separation of carbon disulphide and air is `0^(@)56'`. What is the value of refractive index of carbon disuphide for blue light?

Explanation

Let the refractive index of carbon disulphide for red light = `mu_(r)` and critical angle = `theta_(r)`.
`"Now", " " sintheta_(r) = (1)/(1.634) = 0.6119 = sin37.73^(@)`
`therefore " " theta_(r) = 37.73^(@)`
Let the critical angle for blue light be `theta_(b)`. Refractive increases as wavelength of light decreases so critical decreases.
`therefore " " theta_(c) lt theta_(r)`
According to the question,
`theta_(b) = 37.73^(@) - 0^(@)56. = 37.73^(@) - 0^(@).93^(@) = 36.8^(@)`
So refractive index of carbon disulphide for blue light,
`mu_(b) = (1)/(sintheta_(b)) = (1)/(sin36^(@)48.) = (1)/(sin36.8^(@)) = (1)/(0.5999)`
= 1.669