Bending of light concept help

[SadPanda6022]

Homework Statement

In this lab we used a half-circle container filled with water. Multiple angles are given to measure through the liquid in the container, calculating using snell's equation. However I don't understand why we do not have to calculate for the change in the angle from the plastic container?

Homework Equations

why do we not have to account for that?

The Attempt at a Solution

Whent the ray is coming out through the curve I guess it would be like 90 degrees here and it wouldn't change, but I am confused by the top flat portion

pic for reference is attached

 

[BvU]

Hello Panda,

Two ways to tackle this: experimentally you can (could) repeat the observations for the half-cylinder without water. And the other thing you can do is look up the index of refraction for some plastics (perspex ?) and decide whether or not it can be ignored..

 

[SadPanda6022]

Hi! Hope all is well with you BvU,

Well it says in the lab manual that it CAN be ignored...but I do not understand why that is?? would it be if the index of refraction is the same as the air before it initially hits? so if n=1 there would be no change...
let see so polymethylmethacrylate plastic has an index of refraction around 1.4, which is greater then air...

We were not told what plastic we were using specifically, just the manual says we can ignore it, bit asks us why?

 

[SadPanda6022]

Hi! Hope all is well with you BvU,

Well it says in the lab manual that it CAN be ignored...but I do not understand why that is?? would it be if the index of refraction is the same as the air before it initially hits? so if n=1 there would be no change...
let see so polymethylmethacrylate plastic has an index of refraction around 1.4, which is greater then air...

We were not told what plastic we were using specifically, just the manual says we can ignore it, bit asks us why?

Edit: I have a feeling it has to do with the way the light hits? I am not sure.

 

[haruspex]

I don't understand why we do not have to calculate for the change in the angle from the plastic container?

Assuming the plastic is reasonably thin, it is effectively a flat sheet with parallel faces. What would you expect the net deflection to be?

 

[SadPanda6022]

Yes, so then I would think the net deflection would be zero, however, wouldn't it be shifted a degree? Perhaps negligible but the ray would be coming in from the top and be exiting at the same angle then? but would be exiting at a lower distance then it entered.

Where the ray comes out would be shifted to the left of where it would come out if it did not deflect at all right?

 

[haruspex]

Yes, so then I would think the net deflection would be zero, however, wouldn't it be shifted a degree? Perhaps negligible but the ray would be coming in from the top and be exiting at the same angle then? but would be exiting at a lower distance then it entered.

Where the ray comes out would be shifted to the left of where it would come out if it did not deflect at all right?

Yes, the line would be shifted. Through the curved portion of the plastic the angle would also change slightly, but so long as the plastic is thin this would not be much.

 

[SadPanda6022]

So in other words as long as whatever your going through is thin enough, the change in the incident angle/refractory angle is negligible?

Where do physicists draw that line? I know it would depend on the precision you are looking for as well but obviously physicists round things off a lot in order to make things easier...or at least that seems to, and it seems to be a running joke concerning physicists. SO, when do we draw the line? when should I start caring about how thick something is? or in what kind of experiment does that matter? Would it be when the index of refraction is significantly higher then the medium from which the incident angle is coming from?

 

[haruspex]

So in other words as long as whatever your going through is thin enough, the change in the incident angle/refractory angle is negligible?

Well, that's not exactly what I meant.
The thinner the plastic, the closer the inner and outer radii are to being equal. Apply the lens equation, and you can see this means that ultimately the ray is not bent at all.
But if instead you had a sawtooth cross section then you could make it progressively thinner while keeping the angles the same by making the teeth closer together. In this case, the deflection angle will persist.