The refractive index of an unknown liquid

[many questions]

1.

A light ray in dense flint glass that has an index of refraction of 1.655 is incident to the glass surface. An UNKNOWN liquid condenses on the glass's surface. Total internal reflection on the glass-liquid interface occurs for a minimum angle of incidence on the glass-liquid interface at 53.7 degrees.

1. what is the refractive index of the unknown liquid?
2. if the liquid is removed, what is the minimum angle of incidence for total internal reflection?
3. for the angle of refraction of the ray into the liquid film?
4. Does a ray emerge from the liquid film into the air above?

assume the glass and liquid have parallel planar surfaces

Homework Equations

speed of light: c=299792458 m/s
planck's constanct: h=6.626*10^-34 J*s= 4.136*10^-15 eV*s
transportation in a medium: v= c/n where n= the index of refraction
index of refraction: n=c/v
total internal reflection: n(1)*sin(theta)(c)=n(2)*sin(90) where n(1)>n(2)
Malus' law: I=I(0)*cos^2(theta)

The Attempt at a Solution

I used the above equations to determine the refractive index of the liquid, but I was getting very odd/ unrealistic answers.
Can you walk me through the problem/ explain what I should do for each step?

[/B]

 

[kuruman]

1.

A light ray in dense flint glass that has an index of refraction of 1.655 is incident to the glass surface. An UNKNOWN liquid condenses on the glass's surface. Total internal reflection on the glass-liquid interface occurs for a minimum angle of incidence on the glass-liquid interface at 53.7 degrees.

1. what is the refractive index of the unknown liquid?
2. if the liquid is removed, what is the minimum angle of incidence for total internal reflection?
3. for the angle of refraction of the ray into the liquid film?
4. Does a ray emerge from the liquid film into the air above?

assume the glass and liquid have parallel planar surfaces

Homework Equations

speed of light: c=299792458 m/s
planck's constanct: h=6.626*10^-34 J*s= 4.136*10^-15 eV*s
transportation in a medium: v= c/n where n= the index of refraction
index of refraction: n=c/v
total internal reflection: n(1)*sin(theta)(c)=n(2)*sin(90) where n(1)>n(2)
Malus' law: I=I(0)*cos^2(theta)

The Attempt at a Solution

I used the above equations to determine the refractive index of the liquid, but I was getting very odd/ unrealistic answers.
Can you walk me through the problem/ explain what I should do for each step?
[/B]

Which of "the above equations" did you use and how? Several of them are totally irrelevant. I suggest that you draw a ray diagram under the conditions described (ray incident at minimum angle of incidence) and then apply one of the above equations that is appropriate to the diagram.