Question

(a) You have an RLC circuit. You are given resistance, inductance, capacitance, and voltage. What equation would you use to find the power dissipated and how would you solve for it?

(b) There is a star with light at a given wavelength, a particular spectral line. You are given wavelength of light in the laboratory, the wavelength of light received from the star, and/ or the speed. What equation would you use to find how fast is the star moving (or if given two of the three, how would you find the third) and how would you solve for it? (clue: Doppler effect)

(c) If you are given a light source with a particular intensity, or electric field, or magnetic field, with a distance, how would you find the value at another distance? Example, if given magnetic field at one distance, how would you find electric field at another distance. If given intensity at one distance, how would you find electric field at the other distance, etc.

(d) a refraction question. Light enters a pane of glass. there is an angle of incidence, there is an index of refraction, and there is the angle at which it comes out of the other side. What equation would you use to solve for or look for a certain angle and how would you do it?

Answer 1

a) power dissipated = V^2/ Z

where V = voltage

Z = impedance

Z = sqrt(R^2 + (Xl - Xc)^2)

where R = resistance

Xl = inductive reactance = 2pi*f*L

Xc = capacitive reactance = 1/2pi*f*C

(b) the speed canbe found out by the following equation

λ_O = λ_S(c − v_S)/(c − v_O)

λ_o = observed wavelength
λ _s = constant wavelength from the source
c = constant velocity of the wavefront in the x-direction
v_s = constant velocity of the source along the x-axis
v_o = constant velocity of the observer along the x-axis

(d) for finding the angle we use Snell's law

n1sin i = n2 sin r

where n1= refractive index of first medium

i = angle of incidence

n2 = refractive index of second medium

r = angle of refraction