# Geometric Optics: Speed of light and Reflection in a glass cube

## Homework Statement

A large cube of glass has a metal reflector on one face and water on an adjoining face (the figure). A light beam strikes the reflector, as shown. You observe that as you gradually increase the angle of the light beam, if Theta is greater than 58.7 no light enters the water.

What is the speed of light in this glass?

Figure:
http://session.masteringphysics.com/problemAsset/1055385/3/YF-33-54.jpg

n=c/v

n=1.52 for glass

## The Attempt at a Solution

I'm not really sure which way to approach this problem. I initially thought of using n=c/v

1.52=3*10^8/v
v=1.97*10^8 m/s.

This answer is wrong, and I can't see what I'm doing wrong. Any advice would be appreciated.

## The Attempt at a Solution

Redbelly98
Staff Emeritus
Homework Helper
Different types of glass have different refractive indexes, apparently for this cube it is not 1.52.

Instead, have a look at the discussion of Total Internal Reflection in your textbook or class notes -- hopefully that should clear things up.

Hey,

See
Initially Always try solving the problem with values you have been provided with.

In case you feel they are not enough, create new values in terms of variable, like lets take refractive index of water/glass as u.This way in the end if some one told you that it wasn't glass and water and rather glass and oil you will not have to go through the pain of solving again. you could plug in the values in your final expression :-)

Also logic dictates that if we knew about the absolute refractive index of glass, we could calculate the speed directly using v=c/u(glass wrt vacuum).

The question is infact asking you to find the u(glass wrt vacuum) so that you can find speed in the next step.

So moving on,

What is the relationship between theta and angle of incidence on water.

what will the refracted angle be in terms of u and theta.

What happens when angle theta on glass reaches 58.7 degrees?

Last edited:
the light must be totally internall reflected at the glass/water boundary which enables you to calculate n for glass to water. If you take n for air to water to be 1.33 then you can find n for air to glass and therefore the speed in glass.
Were you given n for air to water? or are you expected to look it up or know it?
For this set up I got n for air to glass to be 1.55

I think I understand: sin(ThetaCritical)=n2/n1

sin(58.7)=1.33/n1

n1=1.5565

Then:

n1=c/v

1.5565=3*10^8/v

v=1.927*10^8 m/s

Thank you for directing me to Total internal reflection, does the rest look correct?

Yes, you have got all your formula's right :-)