Can Polaroid Filters Affect Light Transmission Percentages?

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Plz help me For these physics problems!

Plz help me For these physics problems! Plz give me the solutions. Thank you.

1. Vertically polarized light is passed through three successive polaroid filters. The transmission axes are at 30, 60, and 30 degrees to the vertical. What percentage of the light gets through?

2. What value of n is associated with the lyman series line in hydrogen with lamda = 96 nm? Could it be any other series? Explain?
 
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Annie, no one is going to "give" you the solutions. I'll give you a hint for #1 though.

1) Look for a relationship between light intensity and polarizer angle. Then realize that the output intensity from one polarizer is the input intensity for the next polarizer in sequence (but be careful with the angle on the successive polarizers).
 
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Thread 'Need help understanding this figure on energy levels'

This figure is from "Introduction to Quantum Mechanics" by Griffiths (3rd edition). It is available to download. It is from page 142. I am hoping the usual people on this site will give me a hand understanding what is going on in the figure. After the equation (4.50) it says "It is customary to introduce the principal quantum number, ##n##, which simply orders the allowed energies, starting with 1 for the ground state. (see the figure)" I still don't understand the figure :( Here is...
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Thread 'Understanding how to "tack on" the time wiggle factor'

The last problem I posted on QM made it into advanced homework help, that is why I am putting it here. I am sorry for any hassle imposed on the moderators by myself. Part (a) is quite easy. We get $$\sigma_1 = 2\lambda, \mathbf{v}_1 = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \sigma_2 = \lambda, \mathbf{v}_2 = \begin{pmatrix} 1/\sqrt{2} \\ 1/\sqrt{2} \\ 0 \end{pmatrix} \sigma_3 = -\lambda, \mathbf{v}_3 = \begin{pmatrix} 1/\sqrt{2} \\ -1/\sqrt{2} \\ 0 \end{pmatrix} $$ There are two ways...
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