# What angle does the light enter the water in this situation?Light hits the boundary from air into water at an angle of 46 degrees? At what angle does the light enter the water?

crmhaske | College Teacher | (Level 3) Associate Educator

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The answer to this question depends on what the composition of the water is.  Salt water, pure water, and distilled water all have different refractive indices.  How much salt in the water changes the refractive index, how much sediment is in the water changes the refractive index, etc. etc.

The equation to calculate the refractive angle of light passing from one medium to another is:

Ni*sin(Ai)=Nr*sin(Ar), where

Ni - refractive index of the medium light is leaving
Ai - angle the light hits the new medium at
Nr - refractive index of the medium light is entering
Ar - angle the light enters the new medium at

In this case we know that Ai = 46 deg., and Ni and Nr need to be looked up.

For air Ni = 1
For water Nr = 1.33

Subbing what we know into the equation and rearranging we can calculate the angle that the light enters the water at:

sin(Ar) = (Ni/Nr)*sin(Ai) = (1/1.33)*sin(46) = 0.541
Ar = sin^-1(0.541) = 32.7 degrees

Therefore, the air enters the water at 32.7 degrees.