Apiece of glass with a flat surface is at the bottom of a tank of water. if a ray of light traveling in the glass is incident on the interface with the water at an angle with respect to the normal that is greater than 50.0 ∘ , no light is refracted into the water. for smaller angles of incidence, part of the ray is refracted into the water. if the light has wavelenght 408nm in the glass. what is wavelength of the light water?

λ₀ = 542.6 nm

Explanation:

The speed of light is related to the wavelength and the frequency by the equation

      c = λ f

When a beam of light strikes a surface, it makes the electrons in it oscillate, this is a forced oscillation, so the oscillation frequency equals the frequency of the intendent radiation, then the electrons radiate the radiation for a while that absorbed; therefore, the light in both media has the same frequency

As the speed of light changes in each medium, the only way to comply with the equation is for the wavelength of the radiation to change, let's use the definition of the index of refraction

    v =  f

    n = c / v

    n = λ₀ f / f

    n = λ₀ /

    = λ₀ / n

Let's apply this equation to our case

In the glass     λ = 408 nm

In the water is

      = λ₀ / n

    λ₀ =n  

The index of refraction of water-related glass can be obtained by the law of refraction

    Water       glass

   n₁ sin θ₁ = n₂ sin θ₂

For an incident angle of 50º the beam is not refracted in the water, this means that it is parallel to the surface of the glass therefore the angle is 90º, this is called internal total reflection

for angles less than 50º the light that refracts the water that has refractive index 1.33 changes its wavelength

calculate

    =  λ₀ / n

     λ₀ = n  

     λ₀ = 1.33 408

     λ₀ = 542.6 nm

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.