Light after a Polarizer Question

[iurod]

Homework Statement

Initially unpolarized light with an intensity of 240W/m² is incident on a series of two polarizers. What should be the angle between to the axes of the two polarizers such that the transmitted intensity after the second polarizer is 37.5% of the incident one?

Homework Equations

I=I₀cos²$$\theta$$

The Attempt at a Solution

I₁=.5I_ocos²$$\theta$$ (unpolarized light is reduced by halve after the first polarizer)
this can also be written at 2I₁=I_o

We are given that I₂=0.375I₁
2I₁=I_o so I₂ really equals 0.75I₁

0.75I₁ = I₁cos²$$\theta$$
0.75=cos²$$\theta$$
$$\theta$$ = 30 degrees

Did I do this correctly?
Thanks for all your help...

 

[Redbelly98]

Looks good!