Finding Incident Intensity for Unpolarized Light

[wiped_out]

Homework Statement

Two sheets of Polaroid are placed on top of each other with an angle φ between their pass
directions. Calculate be the ratio of transmitted to incident intensity for initially unpolarised
light if φ = 30°.I copied the question exactly, I'm pretty sure that typo wasn't on purpose but I left it there anyway.

Homework Equations

I0 = I'/2

Malus's Law
I = I0 cos^2 θ

The Attempt at a Solution

I used the equation above to do:

= I0 cos^2(30)
cos^2(30)=.75
.75 x .75 = .5625 = 9/16
= I0(9/16)

not sure if that is right

 

[rl.bhat]

When the unpolarised light is transmitted through a Polaroid, 50% of light is transmitted. So I' = Io/2
When it passes through second Polaroid, the intensity of transmitted light is
I" = Io/2*cos^2(θ)

 

[tomcue]

Your attempt at the solution is correct. The ratio of transmitted to incident intensity for initially unpolarized light with an angle of 30° between the pass directions of the two polarizing sheets is 9/16 or approximately 0.5625. This means that only 56.25% of the incident light will be transmitted through the two polarizing sheets. This result can also be obtained by using Malus's Law, which states that the intensity of transmitted light is equal to the initial intensity multiplied by the cosine squared of the angle between the pass directions of the polarizing sheets. Therefore, the intensity of transmitted light would be 75% of the initial intensity, or 0.75 x I0. Taking this into account, the ratio of transmitted to incident intensity would be (0.75 x I0)/I0 = 0.75, which is equivalent to 9/16. This confirms your solution.