Total internal reflection in prism

marpple

1. Homework Statement

Light is incident normally on the short face of a 30-60-90 (degree) prism. A drop of liquid is placed on the hypotenuse of the prism.

If the index of the prism is 1.68, find the maximum index that the liquid may have if the light is to be totally reflected.
2. Homework Equations

sin ik = n1/n2

3. The Attempt at a Solution

sin 60 = n1/1.68

n1= 1.45

it said that my answer is close enough only differ in significant figure. however, they didn't accept my answer. anyone how to solve this problem?? thanks

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Mentor

marpple

i was doing this problem in mastering physic..
and it turned out

"Very close. Check the rounding and number of significant figures in your final answer."

Redbelly98

Staff Emeritus
Homework Helper
Since the calculation gives 1.45492..., it is possible that Mastering Physics made a rounding error and thinks it should be 1.46.

marpple

Since the calculation gives 1.45492..., it is possible that Mastering Physics made a rounding error and thinks it should be 1.46.
OMG..!!
thanks..
it works..

mastering physics sometimes is really killing me with its rounding thingies.. :(

Doc Al

Mentor
Good catch, RB!

mastering physics sometimes is really killing me with its rounding thingies.. :(
You will probably not be surprised to learn that you are not the first to complain about problems with mastering physics. :yuck:

Redbelly98

Staff Emeritus
Homework Helper
It was just a hunch.

If sin(60°)=0.8660... is rounded to 0.87, one gets 1.4616→1.46

Doc Al

Mentor
If sin(60°)=0.8660... is rounded to 0.87, one gets 1.4616→1.46
That's where I was going to go. I wondered if the 60° was meant to be "exact" or really to only 2 sig figs (or 1 ). But if that were true, then the answer should have been rounded to 1.5, which won't fly with Mastering Physics...

marpple

alright... another questions.. still regarding to internal reflection.. :)

A light ray in air strikes the right-angle prism shown in the figure (Intro 1 figure) angle B=32.0. This ray consists of two different wavelengths. When it emerges at face AB, it has been split into two different rays that diverge from each other by 8.50 degree .

Find the index of refraction of the prism for each of the two wavelengths.

so far,, what i did is...

for wavelength one...
n1 sin theta1 = n2 sin theta2
1 . sin 90 = n2 . sin 12
n2 = sin 90 / sin 12 = 4.809

for wavelength two...
n1 sin theta1 = n2 sin theta2
1 . sin 90 = n2 sin (12+8.5)
n2 = sin 90/ sin 20.5 = 2.85

anyone knows where the mistakes are...??
thanks

Doc Al

Mentor
alright... another questions.. still regarding to internal reflection..
This problem has nothing to do with total internal reflection, just plain old refraction. The first refraction is trivial--the rays pass straight through. You only have to worry about the second surface, where it goes from glass to air. What's the angle of incidence at that surface? What are the angles of refraction?

Redbelly98

Staff Emeritus
Homework Helper
That's where I was going to go. I wondered if the 60° was meant to be "exact" or really to only 2 sig figs (or 1 ). But if that were true, then the answer should have been rounded to 1.5, which won't fly with Mastering Physics...
Yes, they (Mastering Physics) have botched this one. It's not uncommon in physics problems to give nice round figures and assume they're "exact", as they seem to have done with the prism angles here.

A commercial prism will typically have better than 0.05 degrees (and sometimes better than 0.01 degrees) tolerance. Not that introductory physics students should be expected to know that!

marpple

This problem has nothing to do with total internal reflection, just plain old refraction. The first refraction is trivial--the rays pass straight through. You only have to worry about the second surface, where it goes from glass to air. What's the angle of incidence at that surface? What are the angles of refraction?
ahh..i thought it was total internal reflection since the ray coming in 90 degree,, but.. for total internal reflection 90 degree should be for the angle of refraction.

so, we dont need to consider from air to glass?
Yes, they (Mastering Physics) have botched this one. It's not uncommon in physics problems to give nice round figures and assume they're "exact", as they seem to have done with the prism angles here.

A commercial prism will typically have better than 0.05 degrees (and sometimes better than 0.01 degrees) tolerance. Not that introductory physics students should be expected to know that!
yess...yess...
blame mastering physics

Doc Al

Mentor
so, we dont need to consider from air to glass?
Nothing to consider. The ray passes straight through (as shown in the diagram) since the angle of incidence is 0 degrees.

All the action takes place at the glass to air surface.

marpple

have to worry about the second surface, where it goes from glass to air. What's the angle of incidence at that surface? What are the angles of refraction?
so, for the first wavelength
the angle of incidence is 32 degree, and the angle of refraction is 12 ??

for the second wavelength
the angle of incidence is 32 degree, and the angle of refraction is 20.5 ??

am i on the right track??

Doc Al

Mentor
so, for the first wavelength
the angle of incidence is 32 degree, and the angle of refraction is 12 ??

for the second wavelength
the angle of incidence is 32 degree, and the angle of refraction is 20.5 ??
Your angles are off. Remember that the angles are measured from the normal to the surface, so you have to figure them out.

marpple

Your angles are off. Remember that the angles are measured from the normal to the surface, so you have to figure them out.
which one is not correct??
the angle of the incidence or the angle of refraction??

Doc Al

Mentor
which one is not correct??
the angle of the incidence or the angle of refraction??
None of them are correct.

marpple

None of them are correct.
LOL

ic,,is this because i took the normal wrongly..??

Doc Al

Mentor
ic,,is this because i took the normal wrongly..??
Beats me, since you didn't show your normal on the diagram. Looks like you took the angle of incidence measured from parallel to the surface instead of normal, and the angles of refraction measured from the horizontal line. :uhh:

marpple

Beats me, since you didn't show your normal on the diagram. Looks like you took the angle of incidence measured from parallel to the surface instead of normal, and the angles of refraction measured from the horizontal line. :uhh:
LOL...
how did you know?? :shy:

ic,, i'll work on it :)

marpple

What's the angle of incidence at that surface? What are the angles of refraction?
well, lemme try again

for the first wavelength
the angle of incidence is 58 degree, and the angle of refraction is 70 ??

for the second wavelength
the angle of incidence is 58 degree, and the angle of refraction is 78.5 ??

Doc Al

Mentor
for the first wavelength
the angle of incidence is 58 degree, and the angle of refraction is 70 ??

for the second wavelength
the angle of incidence is 58 degree, and the angle of refraction is 78.5 ??
Now you're cooking.

Doc Al

Mentor
What values did you get?

marpple

What values did you get?
Find the index of refraction of the prism for each of the two wavelengths.

n1 = 0.902 and n2 = 0.865

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