Calculating Angle of Incidence for Blue Light Using Refractive Index Data

[name_ask17]

Homework Statement

Yellow light strikes a diamond at a 41.0° angle of incidence and is refracted when it enters the diamond. Blue light strikes a piece of flint glass and has the same angle of refraction as does the yellow light in the diamond. See Table 26.2 for data. What is the angle of incidence of the blue light?
Table 26.2
Approx. Color>Wavelength in Vacuum (nm)>Index of Refraction, n
Yellow>580>1.523
Blue>470>1.531

Homework Equations

sin(angle1)n1=sin(angle2)n2

The Attempt at a Solution

sin41=sinx(1.523) then i solved for sinx and get .4307
i plug that in for sinx for----> sin y=sinx(1.531) and get y=41.26 degrees.
this was marked as incorrect. please tell me whrere I am going wrond D:

 

[Redbelly98]

sin41=sinx(1.523)

If that is supposed to refer to the yellow light refracting in diamond, then you need to use the refractive index for diamond. You have used the crown glass refractive index here.

 

[name_ask17]

ok so i did that:
1.523sin 41=2.419sin x1; solved for that and plugged into sin x1 below
1.531sinx2=1.523sinx1 and got:
x2=24.26 and that was also marked wrong :(

 

[Redbelly98]

1.523sin 41=2.419sin x1

Do you think the yellow light travels from the glass into the diamond, or from air into the diamond?

 

[name_ask17]

the air. but how does that affect my equation?
does this mean i don't use the color indicies of refraction at all? i just use the refraction for glass, diamond, and, air?
because by doing that, i get X= 24.397 and that is still not correct.
please advise

 

[Redbelly98]

the air. but how does that affect my equation?

It means you use the refractive index of air, and not of glass, to describe refraction of the ray for the diamond:

1*sin(41.0) = 2.419*sin(x1)​

does this mean i don't use the color indicies of refraction at all? i just use the refraction for glass, diamond, and, air?

Yes, but you have to use the correct refractive index for the glass.

because by doing that, i get X= 24.397 and that is still not correct.
please advise

You're very close. What color is the light that is refracted by the glass? Which refractive index (blue or yellow) did you use in your calculation?

Also ... what level of accuracy (number of digits past the decimal) are appropriate for your final answer?

 

[name_ask17]

can you explain to me why i won't use the refracticve index of yellow for the first part? isn't it saying the yellow light goes into the diamond? why would i use the refractive index of air instead of yellow light?
besides that...
when i do that, my first equation is 1sin41=2.419sinx1; i solve for sinx1 and plug it into sinx2=1.531sinx1 and solve for x2 to get 24.53? is that correct?

 

[Redbelly98]

24.5 degrees is correct

can you explain to me why i won't use the refracticve index of yellow for the first part? isn't it saying the yellow light goes into the diamond? why would i use the refractive index of air instead of yellow light?

You use the refractive index of yellow light in air, which is 1. The 1.523 number is for yellow light in glass. Use 1 whenever the light is in air, no matter what color it is.

besides that...
when i do that, my first equation is 1sin41=2.419sinx1; i solve for sinx1 and plug it into sinx2=1.531sinx1 and solve for x2 to get 24.53? is that correct?

I agree with 24.5 degrees , which is different than the 24.4 degrees you wrote before.

 

[name_ask17]

unfortunately 24.53 was incorrect and that was my last attept possible for this question :/
could you advise where i mightve gone wrong?

 

[Redbelly98]

I agree with your answer, so it appears you did it correctly. Sometimes rounding answers slightly differently, or using the wrong number of significant figures, will make an otherwise correct answer register as the wrong one. I would have given the answer to the nearest tenth of a degree -- 24.5 -- since that was the accuracy of the given angle of 41.0 degrees.

Was the refractive index of diamond given in the problem, or did you look it up somewhere else? Slightly different values might be used by different sources. Here is a list of slightly different numbers for diamond:

http://hypertextbook.com/facts/2005/JaminBennett.shtml

Sorry the problem didn't work out.

 

[name_ask17]

i actually looked it up in my textbook so i will talk to my teacher about it
thank you for all your help