Why Does Total Internal Reflection Not Occur at the Oil-Water Interface?

[roeb]

Homework Statement

Consider a layer of oil assume n = 1.6 about 5 mm thick floating over a body of water n = 1.33. If a light ray is obliquely incident from air onto the oil surface find the range of incidence angles if any that results in total internal reflection at the oil water interface.

Homework Equations

sin(theta_critical) = n2/n1 when n1 > n2

The Attempt at a Solution

My first attempt would be to say that theta_crit = arcsin(1.33/1.6). However, that is incorrect.

My professor said to use snells law and consider each interface.

1*sin(theta_incident) = 1.6 * sin(theta_2)
n2*sin(theta_2) = n3 * sin(theta_3)
1.6*sin(theta2) = sin(theta_i)/1.33 = sin(theta_3)
However, I can't seem to get anything useful out of this...

The answer is that there is no incident angle that would found. I can see that for the air-oil interface 1.6/1 wouldn't have any critical angle, but why does the oil-water interface not have one as well?

 

[rl.bhat]

Find the critical angle between oil-water interface.
Taking this as the angle of refraction in the air-oil interface find the sine of angle of incidence.

 

[nlightner]

I would approach this problem by considering the refractive indices of each medium and the laws of refraction. I would use the formula sin(theta_critical) = n2/n1 to determine the critical angle for the air-oil interface. However, since the refractive index of oil (n=1.6) is greater than that of water (n=1.33), there would be no critical angle for the oil-water interface. This means that there is no range of incidence angles that would result in total internal reflection at the oil-water interface. Total internal reflection only occurs when the incident angle is greater than the critical angle, which is not possible in this scenario. Therefore, all incident angles would result in refraction at the oil-water interface.