Optics: refraction and reflection

[denniszhao]

Homework Statement

I have no idea how to start with this problem. I am trying to look for all the incident angles, refraction and reflection angles. And i don't know what the two radii are doing with y.

Relevant Equations

critical angle = arcsin (n2/n1)
snell's law for refraction: n1sin(theta1)=n2sin(theta2)

Homework Statement: I have no idea how to start with this problem. I am trying to look for all the incident angles, refraction and reflection angles. And i don't know what the two radii are doing with y.
Homework Equations: critical angle = arcsin (n2/n1)
snell's law for refraction: n1sin(theta1)=n2sin(theta2)

A cup with refractive index n2= 1.8 has outer radius b= 6.0 cm and inner radius a= 4.0 cm. It is filled with a liquid with refractive index n3= 1.3. In the surrounding medium with n1= 1.0, a ray of
light travels along a trajectory that is at a perpendicular distance y from the center of the cup. The ray enters the cup and, reaching the liquid interface at the critical angle, undergoes total internal reflection.

 

[tnich]

The first thing to do is to label the diagram with the angles of reflection and refraction. Also draw in the perpendiculars to the surfaces at the points of refraction and reflection (which would both pass through what point?). Once you see what the geometry looks like, you can start with the critical angle and work your through the geometry to get $y$.