Solving Light & Dispersion: Angle of Incidence of Blue Light

[Deidre]

Homework Statement

Yellow light strikes a diamond at a 47.0° 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

sin(47)*(1.523)=sin(angle)*(1.531)
sin(angle)=.7275321
angle=46.6799


************
Argh, thought I knew what I was doing, apparently not

 

[grant9076]

First, I assume that the 1.531 is the index of refraction of blue light in flint.

You have mixed the equations.
let x be the angle of refraction for both the diamond and the flint
let y be the angle of incidence in the flint.

sin(47)=x*1.523 for diamond
and
sin(y)=x*1.531 for flint

You now have 2 equations and 2 variables which you can solve.

 

[m2003]

Hi there! It looks like you've made a good attempt at solving this problem. However, there are a few things that need to be addressed.

Firstly, your equation is correct, but you have used the wrong values for n1 and n2. n1 should be the index of refraction for the medium the light is coming from (in this case, air), and n2 should be the index of refraction for the medium the light is entering (in this case, the diamond). So the equation should be:

sin(47)*(1.00)=sin(angle)*(1.523)

Next, you need to rearrange the equation to solve for the angle of incidence:

sin(angle)=(sin(47)*(1.00))/(1.523)
angle=sin^-1[(sin(47)*(1.00))/(1.523)]
angle=31.91°

So the angle of incidence for the blue light is approximately 31.91°. This is slightly different from your answer of 46.6799°, which I believe may have been a result of rounding errors.

I hope this helps! Keep up the good work in your studies of light and dispersion. :)