A hemispherical light source emits unpolarized light with a sourcepower of 600W.

Question

A hemispherical light source emits unpolarized light with a sourcepower of 600W. The light is incident on a stack of 3 polarizingdiscs (radius 2cm and 0.1mm thickness) located 2m from the source.The polarizing axes of the discs are the y-axis, 45 degrees fromthe origin, and the x-axis, respectively. The discks all touch eachother.
1. Calculate the intensity of the light incident on the firstplate. 2. Derive an expression for the transmitted intensity of thepolarizing stack as a function of time if the middle disc isrotating clockwise with a constant .Assum it startsfrom the y-axis. 3. If each disc has a specific heat similar to Tungsten and adensity similar to carbon, how long will it take to raise thetemperature of the first disc by 50 degree? 4. A container of water is placed justto the right of the third disc. The middle disc rotates with anangular speed of 10s-1. How long will ittake this light source to bring a 0.5L sample of water initially at40 degrees Celcius to a boil? (Consider the average power deliveredover a full period of rotation)
Please showALL work! I promise to rate you aslifesaver if your answers are correct!
1. Calculate the intensity of the light incident on the firstplate. 2. Derive an expression for the transmitted intensity of thepolarizing stack as a function of time if the middle disc isrotating clockwise with a constant .Assum it startsfrom the y-axis. 3. If each disc has a specific heat similar to Tungsten and adensity similar to carbon, how long will it take to raise thetemperature of the first disc by 50 degree? 4. A container of water is placed justto the right of the third disc. The middle disc rotates with anangular speed of 10s-1. How long will ittake this light source to bring a 0.5L sample of water initially at40 degrees Celcius to a boil? (Consider the average power deliveredover a full period of rotation)
Please showALL work! I promise to rate you aslifesaver if your answers are correct!

Explanation / Answer

1. To find the intensity some distance from a source of sphericalwaves, we use I=P/(4r2), but this is ahemispherical source so the energy is only being spread over halfas much area: I=P/(2r2) P=600W, r=2m so I=23.87W/m2. Let's call this I0 2. The intensity between the 1st and 2nd polarizers is I1= 0.5I0=11.94W/m^2, and the E field is polarised in the y direction. The intensity after the 2nd polariser isI2=I1cos2. Now the plate is rotating at a rate ofd/dt=, so we can integrate this and write(t)=t+C. The starting angle is 0 rad (it starts at they-axis which is parallel to the polarisation of the incoming light)so C=0 and (t)=t. Hence I2(t)=I1cos2(t), and the angle of the Efield is t. Now there is still a 3rd polarizer! If the absolute angle of theE-field is =t, the angle of the E-field with respect tothe 3rd polariser is =(90-t) SoI3(t)=I2cos2(90-t)=I1cos2(t)cos2(90-t)=11.94cos2(t)cos2(90-t)W/m^2 Now, I'm just going to submit this answer (my connection is alittle dodgy and I don't want to lose all my typing), but don'tworry, there's more to come.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.