From Snell's law, the angle of refraction is 38 degree approximately and the index of refraction is 1.13
The given refractive index is 1.61
If light approaches the gem at an angle of 80.0°, that means the angle of incidence is 80.0°
To calculate the angle of refraction, we will use Snell's law which state that:
n = sin i / sin r
where n = refractive index
Substitute all the parameters into the formula
1.61 = sin 80 / sin r
make sin r the subject of formula
sin r = sin 80 / 1.61
sin r = 0.611
r = [tex]Sin^{-1}[/tex](0.611)
r = 37.7
r = 38 degree (Approximately)
We will use the same formula to calculate the index of refraction of a material if the angle of incidence is 60° and the angle of refraction is 50°. That is,
n = sin i / sin R
Where n = index of refraction
i = Incidence
R = refraction
Substitute all the parameters to the formula
n = sin 60 / sin 50
n = 0.866 / 0.766
n = 1.13
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