Ray of light striking a plastic sheet

[imatreyu]

Homework Statement

A sheet of plastic, n= 1.5, 25 mm thick is used in a bank teller's window. A ray of light strikes the sheet at an angle of 45 degrees. The ray leaves the sheet at 45 degrees, but at a different location. Use a ray diagram to find the distance between the ray that leaves and the one that would have left if the plastic were not there.

Homework Equations

I understand the entirety of this solution:

http://answers.yahoo.com/question/index?qid=20090410213448AAiL3zm

However, I don't understand the wording of the problem above, which is from my textbook. The yahoo answers solution seems to contradict what the problem says-- and that is that the ray of light leaves at a 45 degree angle if the plastic IS there. However, the link seems to imply that such would occur if the plastic was NOT there. I agree that if the plastic was not there, the light would just keep going at a 45 degree from the normal. So what does this problem mean?

The Attempt at a Solution

I pretty much attempted it the same way the yahoo answers attempts it. ^
I'm having a hard time understanding it because of the way the problem is worded.

Thank you so much in advance!

 

[ehild]

Just try to draw the path of light inside and outside the plastic.

ehild

 

[imatreyu]

I drew the path of light inside, and I figure that without the plastic it would just go straight. With the plastic, I figured that it would be bent and would emerge at some other angle.

Is the problem saying that with plastic the light would go in at a 45 degree angle and come out at a 45 degree angle at another location. . ? So it. . doesn't get bent?

I'm just really confused.

 

[RoyalCat]

That answer is incorrect. It failed to use Snell's Law appropriately. Snell's Law applies both when the ray enters the plastic, and when it exits it.

Trace out the path of the ray if there were no plastic, the yahoo answer got that part right.
Next trace out the path of the ray with the plastic in place, remember to consider the refraction of the ray both as it is going in, and as it is going out. Use Snell's Law to find the relationship between the angles the the ray makes with the normal to the surfaces of the plastic on the way in and out.
Then use geometry to find the distance between the two exit points, and thus, the two exiting rays.

 

[imatreyu]

Ahhh...never thought about that--
Thank you so much to both of you (ehild and RoyalCat)!

 

[Hellabyte]

I drew the path of light inside, and I figure that without the plastic it would just go straight. With the plastic, I figured that it would be bent and would emerge at some other angle.

Is the problem saying that with plastic the light would go in at a 45 degree angle and come out at a 45 degree angle at another location. . ? So it. . doesn't get bent?

I'm just really confused.

When the light comes out of the other end of the glass or whatever, because it is going from glass to air, Snells law will 'work in reverse' and the ray will return to its incident orientation(the angle will be the same).

 

[imatreyu]

Oh, thanks!

So it's 45 degrees in the end?

 

[imatreyu]

Specifically, I found that it ends up coming out at angle of 45. Then I calculated the answer using triangles and the law of sines and I got 11.707 mm as the difference. . Apparently, the answer is actually something like 8.0 mm. I'm so confused. :(

 

[RoyalCat]

I got 11.63 mm, check your unit conversions, since our answers match up to rounding errors.
And yes, the point of the exercise is to show that a ray does not change its orientation when it goes through such a plate, it is only displaced slightly, depending on the width of the plate.

 

[imatreyu]

Thank you so much! (It's 1 AM Hawaii time and I'm relieved now. . .haha) Thank you again!