# 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?

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### 1 Answer

**Answer: 47.5°**

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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