Question

Waves help please?

A scientist notices that an oil slick floating on water when viewed from above has many different rainbow colors reflecting off the surface. She aims a spectrometer at a particular spot and measures the wavelength to be 750 nm (in air). The index of refraction of water is 1.33.

Answer 1

The index of refraction of the oil is 1.20. What is the minimum thickness t of the oil slick at that spot?

Answer 2

E&M eh?

Answer 3

and optics

Answer 4

I do not understand this question at all :/

Answer 5

do you know what the index of refraction represents

Answer 6

@roadjester what do you mean by E&M?

Answer 7

Electricity and Magnetism. usually E&M goes together with Optics

Answer 8

@roadjester speed of light in vacuum / speed of light in material?

Answer 9

By the way, the answer is supposed to be 313

Answer 10

ok, first of all, do you know what the definition of the index of refraction is?

Answer 11

Not entirely sure to be honest

Answer 12

How much the speed of a wave slows down?

Answer 13

ok, the index of refraction is a unitless number that is defined as

n=c/v
where n is the index of refraction, c is the speed of light, and v is the speed of light through a medium

Answer 14

Right

Answer 15

the speed of light in vacumn is 3 X 10^8 m/s, and the speed of light through water is about 2.25. Light slows down in water because it is more "optically dense".

Now then, for your question

Answer 16

the denseness of oil is not uniform. When the light passes through the oil, it then hits the water underneath it. This causes kind of like a "flip" if you will of the wave. This in turn is what causes the rainbow.

Do you recall an example of attaching a rope or string to a wall and then sending a wave down that rope or string?

Answer 17

Yes I do

Answer 18

And you notice that when the rope hits the wall, the returning wave will "flip" correct?

Answer 19

Yep!

Answer 20

Sorry, be back in a bit, need to take care of something

Answer 21

Of course

Answer 22

Is it ok if I check back in around 30 minutes as well?

Answer 23

ok back; sure go ahead

Answer 24

I am back as well

Answer 25

was there an angle given? the angle that the light is aimed at the oil slick?

Answer 26

Nope

Answer 27

There was this hint : Hint 1. Thin-film interference
In thin films, there are interference effects because light reflects off the two different surfaces of the film. In this problem, the scientist observes the light that reflects off the air-oil interface and off the oil-water interface. Think about the phase difference created between these two rays. The phase difference will arise from differences in path length, as well as differences that are introduced by certain types of reflection. Recall that if the phase difference between two waves is 2π (a full wavelength) then the waves interfere constructively, whereas if the phase difference is π (half of a wavelength) the waves interfere destructively.

Answer 28

I am thinking about asking my professor tomorrow, so if this is too time consuming, don't worry about it :)

Answer 29

Hmm, ok, so I've been going about this kind of wrong. This is wave optics, not ray optics. Oh you said wave help. duh

Answer 30

Give me one sec to refresh my memory on wave optics. I'm not as good at wave optics though so one sec.

Answer 31

Of course, thank you :)

Answer 32

2t = (m + 1/2) lambda
t is the thickness of the film, in this case, the oil
m is a constant 0, 1, 2...
and lambda is the wavelength

Answer 33

this is for constructive interference

i'm not too sure on how to explain it since i'm not that good with electromagnetic waves, but if you solve for t, but don't divide by 2, you get 312.5 which is your answer

Answer 34

sorry i could be more help

Answer 35

hmmm, that equation may be helpful for me. I'll try to think about it a bit more. Thanks for helping

Answer 36

@pottersheep
The reflected wave has a phase change of π when the 2nd medium is denser (I find wave reflection/transmission in close resemblance to collision).

So, the concerned wave undergoes transmission in air-oil interface and reflection in oil-water interface.

As there is never a phase change in case of transmission; we need to get a path difference corresponding to a phase change of π (as we'll already get a phase change of π from reflection).

Answer 37

*got