predictcalculate-a-film-of-oil-with-an-index-of-refraction-of-148-and-a-thickness-of-150-mathrmcm-fl

Question

Predict/Calculate A film of oil, with an index of refraction of 1.48 and a thickness of $1.50 \mathrm{cm},$ floats on a pool of water, as
shown in FlGURE $26-74$ . A beam of light is incident on the oil at an angle of $60.0^{\circ}$ to the vertical. (a) Find the angle $	heta$ the light beam
makes with the vertical as it travels through the water. (b) How
does your answer to part (a) depend on the thickness of the oil
film? Explain.

Sheh Lit Chang · Accepted Answer

this question. We have this set up their of oy. Um, it&#x27;s on now. So it&#x27;s not like poor water. And then the beam off light its incident on the oil and and go up incidents off 60 degrees and we want to find and girl reflection, um, It makes it so vertical as it travels through the water. Came the angle data as labor on the diagram. Okay, so to do this problem will be using Snell&#x27;s law heat because it&#x27;s related to reflection. Okay, so we&#x27;re going to live with this. And glass data are and similarly, this angle here, the data are okay. And so, using sounds law, you have, uh, and air is equal to and a times sign 60 degrees is equal to And oy. Sorry. There are. And you also have. Okay, so this is for the or interface, And then we also have the oil water interface, and so you have the effective index off all times. Sine data are is equal to a reflective index of water. Kind of science data. Yeah. So this is the oy water interface. Okay, So, Andi, if you look at this thes two terms are equal So we can, uh, immediately. Right. Uh, and air time sign. 60 degrees is you go to and water. I&#x27;m side data. Okay, so putting the numbers data is equal to science. 60 degrees. You&#x27;re right by 1.3 tree. Okay, which is 0.651 And then data is equal to 40 26 degrees. Yeah. Okay, so this is the answer for party, then in part B, um, is the answer data depend on the thing that soy uh, okay. Data that&#x27;s not depend on the thickness off. Oy, he Yeah, because the the equation that commenced data that&#x27;s not contain any information about the things. Oh, boy. So the answer is that&#x27;s not pen. Okay, Because the equation of use, um is, uh, is this equation so it doesn&#x27;t contain thickness of boy. So, yeah, so it doesn&#x27;t That&#x27;s not depend on the thickness. Okay. And that&#x27;s all

Steven Emmel · Answer

Hello, everyone. This is problem. 83 from chapter 28 says a thin film of oil floats on water when sunlight Isn&#x27;t that right? Angles the film. The Onley colors are absent from the reflected light are blue and red Estimate the thickness of the oil film. Okay. And it gives us the indices of refraction of oil and water and the two wavelengths that we&#x27;re talking about. The blue and the red. Okay, so, um, first of all, drawing out our situation here have film of oil. So this is like an eagle&#x27;s 1.4, and then we have floating on water. Any goals? 1.33 and ah, our theory of the heirs, like n equals one. Okay, so we&#x27;re talking about, of course, Is the interference here of the two reflected race. Okay. And for saying that there are certain ones they&#x27;re absent. So, um, we&#x27;re going to want to, uh, find the condition for having destructive interference in this case. So we do need to think about the, um I think about the face changes at each interface because if, of course, if one raise 180 degrees off, but the other one isn&#x27;t, then Ah, for destructive interference is it would just be m linda. And then, ah, if there in phase here than, uh, this will be m plus 1/2 all times. Lambda. Okay, so, ah, at this first interface, of course, there will be a 180 degree fate face change. So this reflected Ray will be won t off. And then at this year, face there won&#x27;t be Okay, So, uh, remember that this happens because when you go from ah, an area a medium of lower index of refraction to hire index of refraction. So that only happens that the first in your face. And so, um, that means that the condition for destructive interference here is to end. T is equal to m elinda. Okay, So, thickness, then is m linda over to n that will allow for this to happen. And so were given two different lambda cz for which this happens. And of course, we know the thickness must be, you know, the same for each one because we&#x27;re just talking about one physical situation. So we need the M one lambda one over to n is equal to em to Lambda to over to him. Of course. The ends of the same right. They&#x27;re both referring to the end of the whale. And so, by taking the ratio of the two lamb does, for instance, landed two over Lambda One. This gives us what m one over m two should be, and we can easily find um, Well, hopefully hopefully we can easily find integers and wanted em to ah which, um are equal to the ratio of the two lamb jas. So if we take the ratio of the two lands, so we take the bigger Linda Vibe us or let&#x27;s say it&#x27;s more like a divide by the bigger Lambda the Blue Divide Brotherhood for 58/6 87. Um, we&#x27;ll find that this is equal to about 2/3. Should be very, very close to 2/3. Okay, so this means that we can take em illegals to an empty eagles. Three. Um, of course, we can also do a bunch of waken do. Ah, like M one equals four and empty vehicle six. But we&#x27;ll see later. What? Why? We need to take this one. So let&#x27;s just take em illegals to and, um, empty illegals three. And if we go about doing that Ah, we find that our thickness is approximately 491 nanometers. So plug that back into here. Of course, you can take em one. If you use someone, you have to use it with Lambda one. And if you take em to you after you use it with Lambda too. But of course, no matter which one. You d&#x27;oh! I should be the same, cause someone Linda wants equal time to Linda too. So either one, you should get 491 meters. Uh, now, how do you know it&#x27;s not some multiple off this? And in fact, it could be any energy multiple 491 nanometers positive. Of course, s so how you know it&#x27;s not a bigger one. Well, as the thickness becomes creator, their arm or ah, they&#x27;re more wavelength, which destructively interfere upon reflection and so fund that if you take um twice a sickness, for example, there will be at least one more, um, at least one more way of life which destructively interferes while in the problem. It does clearly state that Ah, the Onley colors they&#x27;re absent are the blue and the red. Okay, so this is That&#x27;s pretty key. And so that means that the thickness must be the smallest, smallest one that you confined not just, uh, a larger multiple.

Adnan Gill · Answer

So we have a layer off oil and then underneath the oiler some liquid. So let&#x27;s run a normal year. Light comes in through the oil on the handle of 64 degrees, and it keeps moving through liquid at an angle of 53 degrees. So the refractive index off the oil is given as 1.45 and the refractive index off the liquid is unknown. So Snell&#x27;s law would say, end too sign of failure to is equal to end. One sign of theater. One so and two is what we&#x27;re trying to figure out. So end to time sign off. 53 degrees is equal to 1.45 times the sign off 64 degrees. So solving for end, you get value one point 63

Farhanul Hasan · Answer

hard for part air strongly, strongly reflected means constructive influence. So we know that two times anti is equal to M plus half looks m plus half um, Lambda, uh, but and so Lambda off. Order em will be given by two and t over plus half again. This is for constructive interference. And so plug in 1.45 a. M and two he millimeters for thickness divide by plus half. So you get an expression like equals 812 millimeters over having plus half. And so now you plug in from values of em. So for M equals zero, you have lambda equals, um 16 20 millimeters. So this is in the infrared ir, um, for M equals one lambda will be 5 41 nana meters. So this is green light, and this is a visible or optical. And for M equals two, let&#x27;s see, you have lember equals 3 25 centimeters. So this is and, uh, ultraviolet, so M equals 15 41 nanometers is strongly reflected light in the visible part of the spectrum. And it is, of course, green light. So labeling by 41 color is green. Um, as for de structure. As for strongly transmitted, this is destructive interference. So instead of the first equation here, you have to anti vehicles m Linda. And so therefore, Lambda will just be to anti over em. So this will be a 12 nanometers again over em. The order. And so for M equals one you have Lambda equals 8 12 centimeters. This is still in the infrared. Ah, but for M equals two, you have Lambda equals 406 nanometers. So this is in the visible and this is the This is my strongly reflected and this is blue light. This is the most commonly transmitted I should say.

Zachary Warner · Answer

our question wants us to consider an oil film on water with an index of refraction in equal to 1.45 in the film has a thickness t equal to 280 nanometers says for part a find the wavelength in color of light in the visible spread spectrum that is most strongly reflected. Okay, so for reflection, the most strong reflection we&#x27;re gonna use the equation two times. In times the thickness is equal to in plus 1/2 multiplied by Lambda. Okay, so we&#x27;re gonna start here with M equals zero. Um, actually, it&#x27;s Go ahead, organize it this way. So for M equals zero we saw for Linda, we see that lambda is equal to two times in times t divided by 1/2. For another words, Lambda is equal to 1600 in 24 nano meters. But that is outside the visible spectrum. So that can&#x27;t be the answer because it wants inside the visible spectrum. So next let&#x27;s do Let&#x27;s try the next one and equal to one. Well, if m is equal to one, then Lambda is equal to two times in times T divided by one plus 1/2 or divided by three halfs. So the two times in times T divided by three halves this comes out people. 541 nano meters. You can look this up if you want, but 541 mana meters is the equivalent to a green light, so this could be boxed in. Is your solution for part a. Okay? Part B says to find the wave length and color of light in the physicals visible spectrum that&#x27;s most strongly transmitted. Okay, so the part that&#x27;s in the visible spectrum that&#x27;s most strongly transmitted is going to be, uh, using the equation two times in times T is equal to in times Lambda. But, uh, since we&#x27;re considering what&#x27;s being transmitted or the conditions for what we would call, uh, destructive interference in has to be equal to 123 or four, it doesn&#x27;t start at zero. So let&#x27;s start a M equals one. So for in equals one, we find that Lambda is equal to two times and times t. It&#x27;s a plugging those values, and we find that Lambda is equal to 812 nano meters. But again, this is outside of the visible spectrum. So we need to find the next one up so we&#x27;ll go to M equals two. If in equals to Lambda is equal to two times in times T divided by two. So the two cancel and this is just 10 times T, which comes out to eagle. 406 nano meters. 406 nano meters corresponds to light. That&#x27;s in the violet part of the spectrum. This is violet light making box said it is their solution for part B in the final solution for our question.

Ryan Hood · Answer

this throne is just a simple application of cells. Law Snow&#x27;s long tells us that in a times the sign of a is equal to n b timesthe sign of they&#x27;d be. And now let&#x27;s write out what we know here. We know that in a is equal to in oil the index of refraction, of the oil and in the is water. So it&#x27;s 1.333 We also know that the incident angle here with respect than normal is equal to 30 degrees. And the refractive angle with respect to the normal is 45 degrees. And so now, ready to plug this end and solve for in oil This gives in oil is equal to N B times. Sign there, Toby. Over some today. And so we conclude these values and we did 1.89 for in oil. And so this is the final answer

Problem

FlGURE $26-75$ shows a ray of light entering one …

Problem 96 Easy Difficulty

Answer

(a) 40.6 $\mathrm{deg}$
(b) see explanation

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(a) 40.6 $\mathrm{deg}$(b) see explanation

Physics

Elyse G.

Christina K.

Jared E.

Meghan M.

Wave Optics - Intro

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James S. WalkerPhysics

Elyse G.

Christina K.

Jared E.

Meghan M.

(a) 40.6 $\mathrm{deg}$
(b) see explanation

James S. Walker

Physics