Solving Refraction Problems: Calculating Refractive Index of Glass and Juice

[jsmith613]

Homework Statement

A ray of light is passed through a prism and the critical angle is measured
a) If the critical angle for the glass-air boundary is 41 degrees, calculate glasses refractive index
b) the same system as before is used, but this time we measure the refractive index of juice.
If the critical angle of the glass-juice interface is 64 degrees find the refractive index of the juice

Homework Equations

NONE GIVEN

The Attempt at a Solution

I think that for a) I do (1/sin(41)) = 1.52
for b) the refractive index of juice is (1/sin(64)) = 1.11

How do I continue from here?

So: μ of glass-air = 1.52; μ of glass-juice = 1.11

find μ of juice?

thanks

 

[jsmith613]

Is there a formula from this point onwards?

 

[Delzac]

Hmmmm, do you know what you are doing when you did this?

" the refractive index of juice is (1/sin(64)) = 1.11 "

 

[Delzac]

And to add on this too:

" (1/sin(41)) = 1.52 "

 

[jsmith613]

And to add on this too:

" (1/sin(41)) = 1.52 "

Yeh

n = 1/sin(c)
c = 41
n = 1/sin(41)
n = 1.52

same for the other one
n = 1/sin(c)
c = 64
n = 1/sin(64)
n = 1.11

 

[Delzac]

Then next would be what does the 1 in 1/ sin(c) represent?

 

[jsmith613]

Then next would be what does the 1 in 1/ sin(c) represent?

its simply the rule of refraction

 

[Delzac]

Not at all. I simple google search on critical angle will land you this formula:

Sin (c) = n1 / n2, where n1= refractive index of less optically dense, and n2 is the denser.

 

[jsmith613]

Not at all. I simple google search on critical angle will land you this formula:

Sin (c) = n1 / n2, where n1= refractive index of less optically dense, and n2 is the denser.

oh so I just do 1.52/1.11

 

[Delzac]

jsmith,

You need to understand what the formula is telling you and not just blindly throw in the numbers.

Your calculations in part b is wrong in the first place.

Please read through this for a complete understanding on critical angle:
http://en.wikipedia.org/wiki/Total_internal_reflection#Critical_angle"

Also, in part b, the light is traveling from the glass to the juice.

delzac

 

[jsmith613]

jsmith,

Your calculations in part b is wrong in the first place.

Also, in part b, the light is traveling from the glass to the juice.

delzac

So what is the correct method?

thanks

 

[Delzac]

After reading the wikipedia page, what are your thoughts?

 

[jsmith613]

After reading the wikipedia page, what are your thoughts?

refractive index 1 / refractive index 2 = critical angle

BUT

we don't know refractive index 1 or 2 because you said my equation was wrong?

 

[Delzac]

We know refractive index in air is 1.

In the first example, you are asked to calculate the refractive index of glasss.

Then in part b, you are asked to calculate refractive index of juice.

In each part they gave you critical angle, and you know at least one refractive index.

 

[jsmith613]

A ray of light is passed through a prism and the critical angle is measured
a) If the critical angle for the glass-air boundary is 41 degrees, calculate glasses refractive index
b) the same system as before is used, but this time we measure the refractive index of juice.
If the critical angle of the glass-juice interface is 64 degrees find the refractive index of the juice

--------------------------------------

a) 1/sin(41) = 1.52

b) 1.52 / sin(64) = 1.69

is that correct