Question

Total internal reflection at the air liquid surface is observed for an unknown liquid when the angle of incidence is 43 degrees. What is the index of refraction of this unknown liquid?

a. 0.68
b. 1.0
c. 1.47
d. 1.59

Answer 1

c. 1.47

Step-by-step explanation:

• Snell's law states that there exists always a fixed relationship between the index of refraction of two transparent media, and the sines of the incident and refraction angles, as follows:

`(n_(i) )/(n_(r) ) = (sin_(\theta r) )/(sin_(\theta i) ) (1)`

• When there is a total internal reflection, this means that light can't go across the border between two media, i.e., the refraction angle is 90º, which means that sin θr = 1
• Since the refraction index for air is 1, i.e. nr =1, this means that (1) , for total internal reflection becomes:

`n_(i) = (1)/(sin_(\theta i) ) = (1)/(sin 43) = 1.47 (2)`