# Light enters a substance from air at an angle of 32 degrees, and continues at an angle of 23 degrees.  What is the index of refraction of the substance?

quirozd | High School Teacher | (Level 3) Adjunct Educator

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This is similar to another post. You can review the concept there - the link is in the reference.

Snell's Law and the Critical angle formula combine...

Make sure to keep track of which object is which. The following formula will work if and only if we make sure that n_2 gt n_1

sin(\theta_c) = sin(\theta_2)/sin(\theta_1)

where n is the index of refraction.

Therefore, we let n_1  = air and n_2 is our substance. This leads us to \theta_1 = 32^o and \theta_2 = 23^o

Thus...

sin(\theta_c) = sin(23)/sin(32) rArr\theta_c = 47.5^o

Hope that helps!

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