Question

What is the critical angle for the interface between water and sodium chloride?

Answer 1

The critical angle between water interface and sodium chloride is 65.64 degrees.

proof

Snell's Law:
n1*sin(theta1) = n2*sin(theta2), where
n1 = refractive index of 1st medium
theta1 = incident angle inside 1st medium
n2 = refractive index of 2nd medium
theta2 = refracted angle inside 2nd medium

At the critical angle, the refracted angle inside the 2nd medium is 90 degrees, and the sine of 90 = 1. The equation reduces to:
n1*sin(theta1) = n2
Solving,
sin(theta1) = n2/n1
To get the angle, we use arcsin:
theta1 = arcsin(n2/n1)

Now we need the refractive index of water and fused quartz. Water is 1.33, fused quartz is ~1.46, so
theta1 = arcsin(n2/n1) = arcsin(1.33/1.46) = 65.64 degrees.