Any Interesting Problems I could try to solve?

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UncertaintyAjay
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What with college essays and things these past few months, I've been a bit physics starved. I am looking for some interesting physics( and mathematics) problems to get my brains physics side whirring again. So please, fire away!
 
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Yeah, but Insights don't have problems. Just quizzes like " Think You Know Richard Feynaman?"
 
The articles are fantastic and I love reading them, but I am looking for something to solve
 
a double slit experiment with a little twist where second slit has defferent width than the first. say wavelength is 500 nm. width of the slits are 10 and 20 microns. distance between center of the slits 100 micron.
the screen is 5 meters from the slit.
where is the central bright and first dark of both sides?
 
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a perfect sphere has perfectly reflective inner surface. drill a hole on its surface and light a laser pointer to it with 25 degree angle to the radius. how many times the laser beam is reflected before it gets out?
 
I like the first one. I've attempted to get the central maxima:d1=10microns, d2 = 20 microns and do= 100 microns. I'm not entirely sure its right though. But its a good sum, I'm enjoying doing this.
IMG_20151128_120335.jpg
 
Actually, hold on a bit, I think I know what I did wrong . messed up the trigonometry big time, just ignore that .
 
This I think is the right one:
IMG_20151128_122353.jpg
 
These are homework type questions, which should be answered in the homework forums, and follow the normal standards of PF, meaning that images of solutions are frowned upon.

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