Your eye is designed to work in air. Surrounding it with water impairs its ability to form images. Consequently, scuba divers wear masks to allow them to form images properly underwater. However, this does affect the perception of distance, as you will calculate. Consider a flat piece of plastic (index of refraction np) with water (index of refraction nw) on one side and air (index of refraction na) on the other. If light is to move from the water into the air, it will be refracted twice: once at the water/plastic interface and once at the plastic/air interface.
Part A
If the light strikes the plastic (from the water) at an angle θw , at what angle θa does it emerge from the plastic (into the air)?
Express your answer in terms of nw , np , na , and θw . Remember that the inverse sine of a number x should be entered as asin(x) in the answer box.
Part B
What is the distance to the object in terms of θw and l ?
Express your answer in terms of θw and l .
Part C
If the distance to the object is more than about 0.4 m , then you can use the small-angle approximation tan(θ)≈θ . What is the formula for the distance D to the object, if you make use of this approximation?
Express your answer in terms of θw and l .
Part D
Now use the expression found in Part C for the distance between your eyes and the object at point O, and find the ratio of the apparent distance to the real distance, d/D . Remember that the apparent distance is the distance calculated by your eyes using the angle θa instead of the angle θw . Since we are dealing with small angles, you may use the approximations sin(x)≈x and asin(x)≈x .
Express your answer in terms of nw and na .

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.

d) physical means can be used to separate the components of air.

moisture is lackin, and organic acids are scarce.