Refraction and Magnification of a Coin in a Glass Cylinder

[Speedking96]

Homework Statement

A penny is placed at the bottom of a glass cylinder that is 30 cm in height. If the cyclinder is filled to 2/5 its volume:

How much closer to an eye does the coin appear when viewed from directly above?


2. The attempt at a solution

I don't quite know how to approach this problem but since we are studying refraction, I'm guessing it has to do with it.

n _water = 1.33

Can that be considered the "magnification"?

12 cm / 1.33 = 9 cm

So, it appears to be 3 cm above the bottom surface?

 

[Simon Bridge]

Homework Statement

A penny is placed at the bottom of a glass cylinder that is 30 cm in height. If the cyclinder is filled to 2/5 its volume:

How much closer to an eye does the coin appear when viewed from directly above?


2. The attempt at a solution

I don't quite know how to approach this problem but since we are studying refraction, I'm guessing it has to do with it.

n _water = 1.33

Can that be considered the "magnification"?

No.

Since you are studying refraction, you should know a law that tells you how light-rays bend when they cross a surface.

Sketch the situation (bottom of glass, coin on the bottom, water surface above...)
Then sketch in two light rays coming from the coin, and headed for different points on the surface ... at the surface they refract differently: draw in the refracted rays.

Now imagine there is an eyeball looking down from above - as far as the ye is concerned, where do those rays appear to come from?

 

[Speedking96]

The rays appear to be coming from beside the coin. The coin seem stretched out.
Are they looking for a numerical answer?

 

[Simon Bridge]

The rays appear to be coming from beside the coin. The coin seem stretched out.

Reality check - put a coin in a glass of water and look at it. Does it appear stretched out?

Try this: draw a dotted line through the center of the coin and perpendicular to the water surface.
Make a small angle to this line, from where it touches the coin - draw a ray for that angle.
Where the ray hits the water surface, draw in a dotted line showing the normal.
Will the ray refract away from or towards the normal (going from water to air)?

Draw in the refracted ray.
Repeat for the same small angle on the other side of the central line.

Or see:
http://www.physicstutorials.org/home/optics/refraction-of-light/apparent-depth-real-depth

 

[Speedking96]

I've figured it out. Thank you for the link.

 

[Simon Bridge]

Well done.