In the figure, a beam of unpolarized light, with intensity 49 W/m 2 , is sent in
ID: 1401702 • Letter: I
Question
In the figure, a beam of unpolarized light, with intensity 49 W/m2, is sent into a system of two polarizing sheets with polarizing directions at angles
1 = 70 and 2 = 90 to the y axis. What is the intensity of the light transmitted by the system?
Wrong: 2.53 W/m^2 and 5.06 W/m^2
Radiation from the Sun reaching Earth (just outside the atmosphere) has an intensity of 1.36 kW/m2. (a) Assuming that Earth (and its atmosphere) behaves like a flat disk perpendicular to the Sun's rays and that all the incident energy is absorbed, calculate the force on Earth due to radiation pressure. (b) For comparison, calculate the force due to the Sun's gravitational attraction. Assume that the speed of light and Earth radius are 2.998 × 108 m/s and 6.37 thousand km respectively.
Wrong: 2.0e31 N
Explanation / Answer
a)
Intensity through first polarizer, I1 = Io/2
= 49/2
= 24.5 W/m^2
Intesity through second polarizer, I2 = I1*cos^2(90-70)
= 24.5*cos^2(20)
= 21.63 W/m^2
2)
a) Radiation pressure whena a wave is 100% obsorbed, P = I/C
= 1.36*10^3/(2.998*10^8)
= 4.536*10^-6 pa
area of disk, A = pi*r^2
= pi*(6.37*10^6)^2
= 1.2747*10^12 m^2
Force due to radiation, Fr = P*A
= 4.536*10^-6*1.2747*10^12
= 5.782*10^6 N
b) gravitaional atrraction between sun and earth
Fg = G*Msun*Me/d^2
= 6.67*10^-11*1.99*10^30*5.98*10^24/(1.496*10^11)^2
= 3.547*10^22 N
Fr/Fg = 5.782*10^6/(3.547*10^22)
= 1.63*10^-16
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