physics please help,,,?

Question

A beam of light is incident from air on the surface of a liquid. If the angle of incidence is 30.0° and the angle of refraction is 19.0°, find the critical angle for the liquid when surrounded by air.
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A speeder tries to explain to the police that the yellow warning lights on the side of the road looked green to her because of the Doppler shift. How fast would she have been traveling if yellow light of wavelength 579 nm had been shifted to green with a wavelength of 552 nm? (Note that, for speeds less than 0.03c, Equation 21.32 will lead to a value for the change of frequency accurate to approximately two significant digits. Accordingly, please enter your response to 2 significant digits.)
please help,, i have no clue.......

Answer 1

Refraction is defined as

Ni/Nr = sin(Ai)/sin(Ar) where

Ni is incident medium indice of refraction
Nr is refractive medium indice of refraction
Ai is incident angle
Ar is refractive angle

Also
sine(critical angle) = Nr/Ni

So Ni/Nr = sin(30)/sin(19) = 1.535

and critical angle is invsine(1/1.535) = 40.62 degrees.

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His speed would need to be

(579 - 552)/579 * speed of light =
50 000 000 km/h

Note that this is a speed of 0.046 c so I don't know if it is compatible with equation 21.32

Anyway it is sufficiently precise to say that the speeder is guilty as charged!!

Answer 2

Can't do the first bit I'm afraid.
As for the speeder- it would help if I knew what eq. 21.32 was, but anyway:
Since the speed of light is constant, from all points of view, the doppler shift presumably follows the tau equation:
n = n(0)[1-(v^2/c^2)]^1/2, where 'n' is your variable, and n(0) is the value of the variable when stationary, v is the speed of the driver, and c is the speed of light. In this case, you need to know what value of 'v' will feed into the equation to turn n(0)= 579 into n= 552.

So, substituting in these numbers:
552 = 579 x [1-(v^2/c^2)]^1/2

Rearrange and simplify:
552/579 = 0.953 = [1-(v^2/c^2)]^1/2
square both sides:
0.953^2 = 0.909 = 1-(v^2/c^2)
Rearrange:
1-0.909 = 0.091 = v^2/c^2
Square root both sides again:
(0.091)^1/2 = 0.302 = v/c. Therefore, she would need to be travelling at 0.302c
c is 186,282 miles per second, so her speed would be 186,282 x 0.302 = 56,221 miles per second.