Question

A hypthetical new mineral: Unobtanium. Unobtanium, when pure, is transparent and is very refractive. When the incident light ray strikes the surface at 45 degrees (sin 45 = 0.71), the refractive measures 12 degrees (sin 12 = 0.21)(all angles are measured from the normal). What is the Refractive Index of unobtanium?

Answer 1

To solve this problem we will use Snell's Optical law which warns that the ratio of the sine of the angle of incidence to the angle of refraction is equivalent to the index of refraction of the material, therefore,

$n = \frac{sin\theta_1}{sin\theta_2}$

$n= \frac{sin45}{sin 12}$

$n = 3.4$

Therefore the refractive index of Unobtanium is 3.4.

Note: I used the full breast values for 45 and 12 (approximately 10 significant figures)