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

• NickP89
In summary: And as I can see you have properly substitued the values in your equations. :)So, Yes the rest looks correct to me. Just as a precautionary step, always double check your equations and substitutions to avoid any silly mistakes.Good Job!In summary, the speed of light in the glass cube can be calculated using the formula n=c/v, where n is the refractive index of air to glass. By using the relationship sin(ThetaCritical)=n2/n1, where ThetaCritical is the critical angle at which total internal reflection occurs, the refractive index of air to glass can be found to be 1.5565. Therefore, the speed of light in the glass cube is approximately 1.927
NickP89

## 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.

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 let's 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 :-)

## What is the speed of light in a vacuum?

The speed of light in a vacuum is approximately 299,792,458 meters per second, or about 670,616,629 miles per hour.

## How does the speed of light change in different mediums?

The speed of light changes depending on the medium it is passing through. In a vacuum, light travels at its maximum speed, but in other mediums such as air, water, or glass, it travels at a slower speed due to the increased density and interactions with particles.

## Why does light change direction when passing through a glass cube?

When light enters a medium with a different refractive index, such as a glass cube, it changes direction due to refraction. This is because the speed of light decreases in the glass, causing it to bend as it passes through.

## What happens to the speed of light when it reflects off a surface?

The speed of light remains constant when it reflects off a surface. However, the direction of the light changes, depending on the angle of incidence and the surface it reflects off of. This is known as the law of reflection.

## How does the speed of light affect the appearance of objects in a glass cube?

The speed of light can affect the appearance of objects in a glass cube by causing them to appear distorted or shifted due to refraction. This is why objects may appear larger or smaller when viewed through different mediums, such as water or glass.

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