What Angle Increases Cloud Intensity Ratio to Three Times Normal?

[ghostops]

Homework Statement

Find the angle ϕ between the filter's polarizing axis and the direction of polarization of light necessary to increase the ratio of the clouds' intensity to that of the blue sky so that it is three times the normal value.
Express your answer in degrees to four significant figures.

Homework Equations

I=I₀cos²ø

I'_s=I_scos²
I'_c=1/2I_c

The Attempt at a Solution

following some hints they gave for this problem I got to Ratio of
I'_c/I'_s=((3/2)I_c)/(I_scos²ø)

from that I need to find ø but I do not know where to go

 

[mfb]

The Attempt at a Solution

following some hints they gave for this problem I got to Ratio of
I'_c/I'_s=((3/2)I_c)/(I_scos²ø)

from that I need to find ø but I do not know where to go

In this equation, can you identify the initial ratio "cloud intensity / blue sky intensity"? You can assign a new variable to it (R, for example).
Can you identify the new ratio "cloud intensity / blue sky intensity"? Call it R'.

Can you find some relation between R and R' based on the problem statement? This will help to solve the equation for ø.

You don't need those new variables, but they make it easier to understand what is going on.