1. crown glass has an index of refraction of 1.52. when light passes through the glass, at which angle to the normal will it be refracted along the surface of the glass-air boundary?
2.glycerine has an index of refraction of 1.473, and liquid water has an index of refraction of 1.333. what is the critical angle for light passing from glycerine to liquid water?

One

I'm assuming (perhaps incorrectly) that the ray is coming in perpendicularly to the surface of the crown glass. The question is a bit ambiguous, so the assumption may not be correct.

If I am correct.

Formula

n1*sin(θ1) = n2*sin(θ2)

Givens

n1 = 1

n2 = 1.52

θ1 = 90 degrees.

θ2 =  ?

Solution

1 * 1 = 1.52 * sin(θ2)

1/1.52 = sin(θ2)

0.6578 = sin(θ2)

θ2 = sin-1(0.6578)

θ2 = 41.14 degrees.

Two

The critical angle is the one that produces 90o as the exit point. The formula is the same for this question as it was for the first question

Givens

n1 = 1.473

n2 = 1.33

θ1 = ?

θ2 = 90o

Solution

1.473 sin(θ1) = 1.333 Sin(90)

sin(θ1)  =  1.333 / 1.473  * 1

sin(θ1) = 0.90496

θ1 = sin-1(0.90496)

θ1 = 64.82 degrees

elly's long hair:

a. if the salon only takes cash, then this isn't the problem. it doesn't matter how much she has in her checking account.   she can't get a haircut until she has the cash.

b. if she has overdraft protection, then there's no problem.   she can go ahead and write a check that her account can't cover, then sometime later, pay the bank some outrageous usury for loaning her a few bucks for a few days, but with beautiful hair.

c. if elly has some principles, and doesn't want to write a bad check, then now she has a problem.   her desire for the new hairstyle is in conflict with her honesty and integrity.

d.   if the bank will not process a check she writes, then even if she had a million $$ in her account, she couldn't use any of it.   the amount she has in her account is not the problem.   and if i may suggest, she might as well close her checking account, and put the money where it'll work for her.   it's not doing her a bit of good in a checking account, since she can't write any checks.

justin can't pay the full balance:

a. he can't even handle the credit limit he has now.   under no circumstances should he ask for a higher limit.

b.   he can ask for the grace period to be extended.   but that's no solution, the bank will almost certainly refuse anyway, and there are much better options.   he knew the rules of his credit card when he started using it.

c.   he definitely should pay the interest on the balance, plus as much of the balance as he can cover at the same time.

d.   he definitely should pay the minimum otherwise they could shut down his card.   he should also pay as much more as he possibly can.   he should also remember the awkward situation he's in, stop buying stuff on credit that he can't afford, and avoid adding any more debt.

i'd say that justin's best best option isn't on this list of choices.   what he has to do:   pay as much as he can at least the minimum payment plus as much more as he can and then avoid adding more debt.