How Far Apart Are the Rays of Red and Violet Light When Exiting Flint Glass?

[doverdt75]

A ray of white light strikes the surface of a 4.0-cm-thick slab of flint glass as shown in the figure. As the ray enters the glass, it is dispersed into its constituent colors. Estimate how far apart the rays of deepest red and deepest violet light are as they exit the bottom surface. the light is going into the glass at a 60 degree angle... have been working on this one all night just do not know how to begin

 

[ideasrule]

First, dispersion occurs because the glass's refractive index is different for red light than for blue light. The first thing you need to know, then, is glass's refractive index at both ends of the visible spectrum.

 

[doverdt75]

the deepest red is 700nm and the deepest violet is 400nm

 

[kuruman]

the deepest red is 700nm and the deepest violet is 400nm

That is true, but what is the index of refraction for flint glass corresponding to these wavelengths?

 

[doverdt75]

flint Glass has a refraction index of 1.66
Should I be using Snell's Law

 

[kuruman]

Yes, you should be using Snell's Law, but first you need to understand that the refractive index depends on the wavelength. That's what causes dispersion, the splitting of white light into its constituent wavelengths. The value of 1.66 that you found must be some kind of average. You need to find two values of the refractive index, one for 700 nm and another one for 400 nm. Then use Snell's Law for each wavelength separately.

 

[doverdt75]

So I cannot just use 1.66 for both of the numbers
I do not understand what I am supposed to be looking for...
I was thinking v=c/n with c= 3.00*10^8... and n=1.66...?

 

[kuruman]

No you cannot use 1.66 for both. The index of refraction depends on the wavelength of the light. It is only an approximation to say that it is constant. Blue light going from air to glass at an angle bends more than red light incident at the same angle. This means that the index of refraction for blue light is higher than for red light. It is true that v = c/n, but v(blue) < v (red) because n(blue) > n(red). You are supposed to be looking for n(blue = 400 nm) and n(red = 700 nm) in flint glass.

 

[doverdt75]

ok so i found out that deep blue is 1.59 and deep red is 1.54... unsure where to go from there

 

[kuruman]

Use Snell's Law.