Determine the intensity of light passing through a polarizer-analyzer combination with an angle of 45° between them.
assume the incoming light is coming an at an angle theta to the first filter, and assume it is not circular polarization.
light getting through
I*costheta
now the light getting thru the second filter is
I*cosTheta*cos(theta+45)
now if I remember my trig identities that equals
I*(cosTheta(cos(theta)cos45-sinThetasin45)=
I(cos^2theta*cos45-cosTheta*sinTheta*sin45)=
I(.707)(cos^2Theta -cosTheta*SinTheta)=
Now, comparing that to the original incident light, it depends on the incident angle with the first plate. If Theta is zero, then .707 gets thru. If Theta is 90 deg, zero gets thru. You can see the graph here.
http://www.wolframalpha.com/input/?i=plot+y-%3D.707((cos(x)*cos(x)-sin(x)*cos(x))
To determine the intensity of light passing through a polarizer-analyzer combination with an angle of 45° between them, you need to know the initial intensity of the incident light.
Intensity of light passing through a polarizer-analyzer combination can be calculated using Malus's Law, which states that the intensity (I) of light transmitted through a polarizer-analyzer combination is given by:
I = I₀ * cos²(θ)
Where:
- I₀ is the initial intensity of the incident light.
- θ is the angle between the polarizer and the analyzer.
In this case, the angle between the polarizer and the analyzer is 45°. Therefore, substitute this value into the formula:
I = I₀ * cos²(45°)
Now, we need the initial intensity (I₀) of the incident light. This value can be determined from information provided or measured. If the initial intensity is not given, you may need additional information or measurements to find it.
Once you have the initial intensity, substitute it into the formula along with the angle (θ = 45°) to calculate the intensity of light passing through the polarizer-analyzer combination.
Note: It's important to ensure that the angle is measured in the correct units, such as degrees or radians, as required by the formula.