Deviation of wavelengths through barium crown pism

[Liquidxlax]

Homework Statement

The refractive index of an equilateral prism of dense barium crown glass varies with wavelength as given in the table

wavelength (nm)...n

656.3...1.635
486.1...1.646

making use of Cauchy's dispersion formula determine the minimum angle of deviation for sodium light with wavelength = 589.3 nm

Homework Equations

A/2 = theta prime

nsin(theta prime) = sin((A + deviation)/2)

(weird D)/(deviation) = (nf - nc)/(nd-1)

The Attempt at a Solution

2sin^-1((1.635)sin(30)) - 60 = deviation = 49.7 degrees

2sin^-1((1.646)sin(30)) - 60 = deviation = 50.8 degrees

weird D = 50.8 - 49.7 = 11.1 degrees

My problem is that I'm not sure how to find nd to finish the question.

i know i can use

n of wavelength = A + B/(wavelength)^2 + C/(wavelength)^4

but that doesn't leave me with an n between 1.635 and 1.646 and that is my problem

 

[ehild]

You can omit the third term C/(lambda)^4. Find A and B for the two refractive index - wavelength pairs.

ehild

 

[Liquidxlax]

You can omit the third term C/(lambda)^4. Find A and B for the two refractive index - wavelength pairs.

ehild

well I'm not totally sure on this but does this look right, or am i assuming the wrong thing


1.646 = 1.635 + b/((486.3nm)^2)

b = 5.9122x10^-15

then

n = 1.635 + (5.9122x10^-15)/((589.3x10^-9)^2) = 1.652 , but that is greater than 1.646 which is probably wrong then... I really don't know how to solve for A and B. I looked up their values for barium crown glass and it still doesn't work even with those

 

[ehild]

well I'm not totally sure on this but does this look right, or am i assuming the wrong thing


1.646 = 1.635 + b/((486.3nm)^2)

b = 5.9122x10^-15

No, A is not equal to 1.635, why should it?

1.635=A + B/656.3^2

and

1.646 = A + B/486.1^2.

Two equations, two unknowns. Solve.

ehild

 

[Liquidxlax]

No, A is not equal to 1.635, why should it?

1.635=A + B/656.3^2

and

1.646 = A + B/486.1^2.

Two equations, two unknowns. Solve.

ehild

:facepalm: why didn't i think of that... homework is 3x harder when you're sick

 

[Liquidxlax]

Okay i did that and i got a really high number, it seems unreasonable for an angle of deviation, but my textbook examples show ratios of 1/29 1/40... i got for the deviation

643.8 degrees

 

[ehild]

Show what did you get for A and B.

ehild

 

[Liquidxlax]

n1 = A + B/lambda1^2 represent A as a function of B A = n1 - B/lambda1^2
plug this in for A in the second one

n2 = A + b/lambda2^2 then n2 = (n1 - B/lambda1^2) + B/lambda2^2

n2-n1 = B(1/lambda2^2 - 1/lambda1^2) get B = (5.758x10^-15)

Then plug B into either equation solve for A to get A = (1.6216)

Then

n3 = 1.6216 + (5.758x10^-15)/(589.3x10^-9)^2 = 1.638

then plug the rest of the numbers in and solve for deviation in

n3 = nd n1 = nc n2 = nf


(weird D)/(deviation) = (nf-nc)/(nd-1)

deviation = ((weird D)(nd -1))/(nf-nc) = 643.8

 

[ehild]

I do not understand what you did. The question was:

"making use of Cauchy's dispersion formula determine the minimum angle of deviation for sodium light with wavelength = 589.3 nm". You calculated the minimum deviation for the other wavelengths with the equation

2sin^-1(n sin(30)) - 60 = deviation

why do not do the same for 589.3 nm? It is about 50 degrees.

ehild

 

[Liquidxlax]

i'll try that, it seems to make more sense, yet i did the lab on this today and they did it the way i initially was using. But that was a slightly different process.