Calculating Speed of Light in Glass Prism

[DDV805]

Hi, could someone please help me get started on this problem. The figure is a right angle triangle with 30-60-90 degree angles (right angle). Can you help, please. Thank you so much.

The glass prism shown has an index of re-
fraction that depends on the wavelength of
the light that enters it. The index of refrac-
tion is 1.43 and wavelength 7.456 x 10-7 in vacuum and 1.61 for light of wavelength 4.951 x 10-7 m in vacuum. A beam of whitelight is incident from the left, perpendicular to the first surface, as shown in the figure,and is dispersed by the prism into its spectral components.Determine the speed of the 4.951x 10-7 mlight in the glass. Answer in units of m/s.

--------------|30
--->----------|
--------------|
--------------|90___ _60__

 

[clive]

If we use a dispersion relation with only two coefficients,

$$n(\lambda)=A+\frac{B}{\lambda^2}$$

we can find A and B from the input data and find n for the third wavelength. Finally,

$$v=\frac{c}{n}$$.

Hope it helps!

 

[clive]

oops!

I realized your "third" wavelength is identical with the second one...

I'll try to figure out another solution...

 

[clive]

OK, the problem seems easier than I thought:

If you have the index of refraction for a given frequency (or wavelength in vaccum) then you have the velocity from n=c/v. So, v=c/n=3e8/1.61 m/s.

 

[DDV805]

Got it.

Thanks. Very Helpful.