Snell's law through three layers?

[MCATPhys]

A piece of gallium phosphide is frozen in ice. a beam of light is directed downward through the ice-gallium phosphide boundary at a 25 degree angle from the normal. The light emerges from the gallium phosphide 12.25 mm away from where it would have had the solid been pure ice. Find the thickness of the gallium phosphide layer. Gallium phosphide has the highest known optical density (3.5), and ice has the third lowest (1.31).

I know this question is supposed to be easy in that we need to apply snell's law. but can someone please draw an image of what it looks like... because i have no idea what they are asking... is the ice layer on top of the gallium layer...

 

[tiny-tim]

Hi MCATPhys!

It's the same as if the question asked about a piece of gallium phosphide in air, with light hitting it at 25º …

but instead of air, there's ice. ​

 

[MCATPhys]

Hi MCATPhys!

It's the same as if the question asked about a piece of gallium phosphide in air, with light hitting it at 25º …

but instead of air, there's ice. ​

So...

(1.31)sin25 = 3.5sinx
x = 9.10 degrees

then... tan9.10 = 12.25/height
height = 76.5 mm

Is that right? But the book says the answer is 42.2 mm.

 

[tiny-tim]

then... tan9.10 = 12.25/height

ah … but 12.25 isn't the distance from the normal, it's the distance from the 25º line.

 

[MCATPhys]

it's the distance from the 25º line.

I really don't get it... :((((

 

[tiny-tim]

If the gallium phosphide wasn't there (so the light was going through pure ice), then the light would continue at 25º.

The question says that the light is 12.25 mm away from that line.

 

[MCATPhys]

but how do i calculate the distance from the normal the ray of light travels in ice. I'm guessing I subtract that number from 12.55 to get the actual distance.

btw.. thanks so much for helping me

 

[tiny-tim]

If the thickness is d, then the light would have traveled dtan25º from the normal.

(btw, is it 12.25 or 12.55?)

 

[MCATPhys]

okay... that means the light in the phosphide traveled dtan25 + 12.25...

so...
tan9.10 = (dtan25 + 12.25)/d
d = -40.0 mm

I suppose that's close enough to the right answer. I checked the question in the book again.. and it says 12.25 - does that sound wrong?

 

[tiny-tim]

Hi MCATPhys!

(just got up :zzz: …)

… I checked the question in the book again.. and it says 12.25 - does that sound wrong?

No, I only asked because you wrote 12.55 in your post #6.