Light bends as it moves from one medium to another. If the second medium is more dense than the first, the light bends toward the normal, which is the vector perpendicular to the medium's surface. If the second medium is less dense than the first, the light bends away from the normal. The relative refractive index measures the extent of this refraction. It equals the ratio between the sines of the two angles between the light and the normal.

Find the sine of the angle between the light in the first medium and the normal. If you don't have a scientific calculator, use an online one. If, for instance, light hits the surface of the second medium traveling at 25 degrees from the normal: sin (25) = 0.423.

Find the sine of the angle between the light in the second medium and the normal. If, for instance, light in the second medium travels at 49 degrees from the normal: sin (40) = 0.643.

Divide the answer from Step 2 by the answer to Step 1: 0.643 / 0.423 = 1.52. This is the second medium's refractive index with respect to the first.
References
 Photo Credit Stockbyte/Stockbyte/Getty Images