Unpolarized Light Intensity

[Babylady247]

Unpolarized light from an incandescent lamp has an intensity 176 Cd as measured by a light meter. What is the intensity reading on the meter when two ideal are inserted between the bulb and the meter with their axis of polarization making an angle of θ = 40.0° relative to each other? Express your answer in Cd.


am having some trouble with this problem. Here's what I have so far:

Known info:

Io=28 Cd

Theta= 6o

There are two polarizers, so theta1=6 and theta2=6

Equations:

I= Io/2

Malus' Law: I= Iocos^2theta

Work:

I used this to try and solve and it is wrong...

I = 28/2

I=14

Then

I = 28(cos6)^2 which = 27.7 (at theta1)

but there are two polarizers so 27.7 becomes the new Io for theta2

I=27.7(cos6)^2 which =27.4

So you add them right? 27.7+27.4 which = 55.1?

Where am I getting confused?

 

[Redbelly98]

Welcome to PF.

For starters, the problem statement says 176 Cd and 40.0 degrees. Why are you using 28 Cd and 6 degrees when you work out the problem?

 

[tomcue]

Hi there,

Thank you for sharing your thoughts and work on this problem. It seems like you are on the right track, but there are a few things that need to be clarified.

First, the known info you provided (Io=28 Cd and theta=6o) does not seem to match the given information in the problem (Io=176 Cd and theta=40.0°). Please double check the values to make sure you are using the correct numbers.

Second, when using Malus' Law, the intensity (I) of the light passing through two polarizers at an angle theta should be calculated using the formula I = Io * cos^2(theta), where Io is the initial intensity of the light. In this case, Io=176 Cd, so the intensity for the first polarizer (theta1=40.0°) would be I=176*cos^2(40.0°)=106.7 Cd.

For the second polarizer (theta2=40.0°+40.0°=80.0°), the intensity would be calculated using the intensity of the first polarizer (106.7 Cd) as the new Io, giving us I=106.7*cos^2(80.0°)=26.7 Cd.

Finally, to get the total intensity after passing through both polarizers, we simply add the intensities from each polarizer, giving us a final intensity of 106.7+26.7=133.4 Cd.

I hope this helps clarify the problem for you. Let me know if you have any other questions or concerns. Keep up the good work in your studies!