## Online Course Discussion Forum

### physics fundamental: modern physics lesson 1 Chapter 24 practice quiz #8&9&10

I have no idea how to solve question #8, 9, 10

Hi Hongyu. I'll reply with a few hints and ideas later tonight. Thanks for your patience!

Here's some hints.

For question 8, the angle is actually not needed. Because the light is initially unpolarized (so the waves could have all different angles), the intensity of the light is always decreased by a factor of $2$.

The angle in question 8, however, is relevant to question 9. Recall when the polarization *changes* by an angle of $\theta$, the intensity is given by the equation $I = I_0\cdot \cos^2(\theta)$.

Overall, and as a hint for $10$, let's see what happens with a simple example: What happens when initially unpolarized light with an intensity of $400$ passes through polarizers with angles $0^\circ$, $30^\circ$, and $90^\circ$.

- Since the light starts unpolarized, passing through the first polarizer gives a new intensity of $400\cdot \dfrac{1}{2} = 200$.
- The change in angle from the first to second polarizer is $30^\circ$, so after the second polarizer the intensity is $200\cdot \cos^2(30^\circ) = 200\cdot \dfrac{3}{4} = 150$.
- The change in angle from the second to third polarizer is $60^\circ$, so the final intensity is $150\cdot \cos^2(60^\circ) = 150\cdot \dfrac{1}{4} = 37.5$.

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