Solve Snells Law Problems: Red/Blue Angles, TIR & Light Speed

[ph0bolus]

Homework Statement

1.
Sunlight strikes a piece of crown glass at an angle of incidence of 37.9 degrees. Calculate the difference in the angle of refraction between a red (660 nm) and a blue (470 nm) ray within the glass. The index of refraction is n=1.520 for red and n=1.531 for blue light.

2.
The ray now travels inside the glass. What is the minimum angle of incidence at which the red ray can hit the surface of the glass and become there totally internally reflected and not refracted?


3. [1pt]
A light ray of lambda = 530 nm enters at an angle of incidence of 36.2 degrees from air into a block of plastic. Its angle of refraction is 20.2 degrees. What is the speed of the light inside the plastic?

Homework Equations

1) n(sin theta 1)=n(sin theta 2)

3) sin theta plastic=n air/n plastic

V=C/n

The Attempt at a Solution

For number 3 i keep getting 8.57E8 m/s and the computer keeps telling me it's wrong what am i doing wrong here?

 

[mgb_phys]

3, The speed of light is 3E8m/s - your speed in the plastic must be less than this.
Have you got an equation the wrong way round?
What refractive index did you get for the plastic ( hint something between 1.3-1.9 would be realistic)

 

[ph0bolus]

i took the sin of 20.2 degrees and got .35 for refractive index.

 

[mgb_phys]

No, snell's law says the refractive index is the RATIO of the sines of the angles of incidence and refraction.

n = sin(37.9)/sin(20.2)

As a rough guide, n air=1 water=1.3 most glasses are n=1.4-1.8 the hightest natural material is diamond=2.4
Any refractive index outside this range is rare.

 

[ph0bolus]

Ok 1.8 seems to be the refractive index so now to find the speed of light inside the medium i plug in 1.8 into V= speed of light/ n= 3.00E8/1.8= 1.67E8 m/s. The computer still says it's wrong though.

 

[mgb_phys]

Thats the correct way of doing it. Refractive index is the ratio of the speed of light in the material to it's speed in vacuum. Is the computer expecting more significant figures?

 

[ph0bolus]

i got it right i just didnt round it up right or something. Thanks for the help.

any insight on #1 & 2?

 

[mgb_phys]

1 - is just snells law sin(incidence)/sin(refracted) = n
It gives you n for both colours, they have the same incidence, just work out the refracted angles and subtract them.
Or rearrange the equations and use trig identiites to get a-b from sin(a) and sin(b) if you want to show off.

2, The angle that a ray is totally internally relected is called the "critical angle"
The sin of this angle is the ratio of the two refractive index.

 

[ph0bolus]

for #2
sin theta crit= n less dense/ n more dense so,

1.520/1.531 gives me .993

you said take the sin of the ratio and that gives me .017. Shouldnt i have taken the inverse sin of it? If so what after that?

 

[mgb_phys]

It's the ratio of the refractive index of the glass and the other medium (in this case air so n=1 nearly )

sin( critical angle ) = n2/n1 = 1/1.520, therefore angle = 41.4 deg
(it's easy to work out which way up because sin<1.0 )

The confusion is that they have given you two refractive indexes for the different wavelengths, the critical angle will be different for each - it's not clear from the question which wavelength they want the answer for.

 

[ph0bolus]

Ok i got you now. I'll just figure out both of the angles and see which one fits.

Thanks for your help you're a lifesaver