the-index-of-refraction-for-red-light-in-a-certain-liquid-is-1305-the-index-of-refraction-for-violet

Question

The index of refraction for red light in a certain liquid is 1.305 the index of refraction for violet light in the same liquid is 1.336 .
Find the dispersion $\left(	heta_{v}-	heta_{r}ight)$ for red and violet light when both are
incident from air onto the flat surface of the liquid at an angle of
$45.00^{\circ}$ to the normal.

William Affel · Accepted Answer

all right. So if this problem red and violently or both incident on a liquid from air and we want to find the dispersion between the two, the way we&#x27;re gonna find the dispersion between the two is first we have to find the index of refraction of each the red and violet light, using the fact that the incident angle it&#x27;s 45 degrees. The index of refraction of ares, about one and each have their own index of refraction into this liquid. The violent next fraction is 1.336 and the red index of refraction of is 1.305 So we&#x27;re gonna find the dispersion were, first confined, the angle over fraction of the red light. So I want to say the end of air times the sign of 45 would be equal to the index of refraction of the red light 1.305 times the sign of the income of the angle of a fraction of red light. Now, because the index of refraction of ares about one, we just cancel that out, and we can say that the angle over a fraction of red light, evil too. The inverse sign of signed 45 over 1.3 or five, and that should give you an answer. The 32 0.81 degrees that&#x27;s the angle of refraction of the red late from the normal. Now let&#x27;s find the angle over fraction of the blue light, wherein you Snell&#x27;s law again were to say, the index of refraction of air as the sign of 45. It&#x27;s gonna be equal to 1.336 now the index of refraction for the violet light and C sine of the angle of refraction of the light. So now the index of refraction of arable cancel because one I would find the angle refraction of the violet light. It&#x27;s gonna be equal to the inverse sign of signed 45 divided by 1.336 and that should give us an angle of 31 0.96 degrees. Now the dispersion is the difference between these two angles, so we&#x27;re gonna find the difference Team two angles or to say data V minus data are because that&#x27;s how it&#x27;s written in the problem. However, I think the absolute value of it because it&#x27;s just an angle that&#x27;s going to be equal to the absolute value of 31.96 minus 32 going 81 and that should give you a dispersion of 0.85 degrees, and that is our answer.

Adnan Gill · Answer

so we have in prison, which is an equal electric prison, which means that each angle is 16 please. And on this prison we have a great off light, which is sitting at an angle of 60 degrees. So after the light goes in it, way to refract, giving us this angle, they like to. So then we can find we need to do some work to find this angle Table three. And then once we have data three, then we need to find this data four. So that&#x27;s that&#x27;s what we need to do. So four thing is, let&#x27;s do this for a red light. So if this is red light then and one is equal to one since its air and the question says that the Refractive index n toe for Red Light is equal to 1.662 so we can now say anyone sign off 60 is equal to end to time. Sign off failure to so end to his 1.662 So one time sign off 16 is equal to 1.662 times. Sign off to so something this for failure to gives me director is equal to 31.4 degrees. So if they do is equal to 31.4 increased and we can find this angle. This would be a 90 take away 31.4. So this angle is 58.6 degrees and therefore we can then find this angle here, and this angle is 61.4 degrees, which then means that Taylor three is equal to there are three years ago to 28.6 decrease. So how did I get 58.6 degrees? Failure to plus 58.6 degrees is equal to 90 degrees, and then the three angles in a triangle is equal to 180 degrees, so that has been fined 61.4 degrees. So now I can find data four and two times. Sign up. Feel three is equal to 10 1 time sign off. Therefore, so n two is 1.662 times Sign off their A three, which is just that the left he was 28.6 degrees and that is equal to one times sign off, therefore, so solving this gives me theater. Four is equal to 52.7 degrees. So now we need to do exactly the same thing for Violet Light. So let&#x27;s go on an X ray. So we have now again the same prison. We have area flight, which is incident on this face afternoon angle of 60 degrees. But now this is violent. Let and the value off end to now is 1.698 So the first thing we do is find this angle Taylor tools. So we have end to time. Sign off. Syracuse is equal to end One sign off terawatt. So end to is a 1.698 time sign off. Two is equal to one times sign off 60 degrees, so they have to comes out to be equal to 36.7 TV&#x27;s now. Since we know do we can subtract erupting from 90 to get this angle which would be 59.3 degrees and then the three ambulance right in a triangle add up to 180 degrees, which means this angle with people to 16 point 70 reason. And that means that my fellow etc. Right here will be equal to 90 minus 60.7. So Hillary is 90 degrees, minus 16.7 degrees. So that&#x27;s equal to 29 points. Three degrees. And now we can find this angle theater for so n two times sign off. Their A three is equal to 10 1 time sign of failure. Four. So then, to this 1.698 times the sign off Ah, directory was equal to 29.3 degrees is equal to one times sign of data. Four. So something that for theater for the estate are four is equal to 56.2 degrees.

Konstantin Pavlovskii · Answer

in order to solve this problem the ago to use the well known snails law when l I three goes from medium A to medium, be then this sign off The angle of refraction is equal to the ratio off refractive in dishes multiplied by this sign over the angle of incidence here and they is the refractive index off medium A and be is the refractive index off medium. Be off. Our is the angle of refraction. Off I is the angle of incidence. Let&#x27;s isolate off our from this equation Off r equals arc science off the right side in our program and they equals one because medium a is the air, the angle of incidence ecos toe 83 degrees and the for the red camp Orania equals 1.331 and be for the blue Californians because 1.340 the angle of refraction for the red component You closed our side 10 where 1.331 multiplied by this sign off 83 degrees. The angle of refraction for the blue component equals are excited off one or 1.340 multiplied by this sign off the same angle. It is three degrees. The angle of refraction for the red component equals 48.2 degrees. The angle of refraction for the blue component equals 47.8 degrees. Note that I have rounded both on first. So three significant figures This is the final aunts for

Adnan Gill · Answer

So we are told that there is in prison and the anger of here for prison is 25 degrees, and we have a real flight being incident at 90 degrees angle history is like will travel to the prison and it will hit the slap site of the prison, and the angle of incidents in this case would be equal to 25 countries. And then the ray will corrupt, so we have fade out. One is equal to 25 degrees failure on. Then we have to find out the state of do now, and one is different, depending on the color of the light. But end to will always be one, because the medium outside of prisoners care so now snaps losses. In one sign, data one equals end to sign it, too. So end one kind of sign off. 25 degrees is equal to, and two is one times sign off, too. So that means that we can say it to his recall to sign in worse off and one times sign off 25 degrees. So now that we know the formula, we just need to go and say what its data to for wreck. So for red light with the end, two is equal to so for red, and two is equal to one point 662 so that would be signed in Worse, off 1.662 times. Sign off 25 degrees, and that comes to be equal to 44.60 police nothing to for violet light. So everything would be the same except for the values and to it would be signed and worse. Off end to for Violet is 1.698 in one for a while, it like is 1.698 times. Sign off 25 degrees, and that handle isn&#x27;t go to 44 45.90 degrees.

Zulfiqar Ali · Answer

Let&#x27;s use Snell&#x27;s law will Slim Snell&#x27;s Lloyds and one times sine theta. One sign pita one is equal to and two times signed. Clean it, too. And here Tito once tangle of incidents and Peter to his dangle off the fraction well, Peter two is equal to sign in, worse into and one divided by and to into sign Frida one. Now the two weapons are traveling from the air to the quartz. Therefore, uh, and one is equal to one, and given the pita, one is equal to 50 degrees, no food red light and two is equal to 1.145 fine. Militated to this is equal to sign in worse into one divided by 1.1 for 55 times sign or 50 degrees, and for which is equal to about 31 coined seven succeed 768 degrees and for and two is equal to 1.468 Uh, again, Peter, too, pleaded to, is equal to 31 point for 55 degrees. So for oil it light and physical to 1.468 and Peter too physical, too. 31.455 degrees

Zachary Warner · Answer

So we&#x27;re told that some light enters a crown glass from air. So the index of refraction of the medium it&#x27;s coming from my call in someone is one for the index of refraction of air, and the angle of incidence is fatal. One, which is 60 degrees, and the index of refraction were told of the red light, which I call in to our. So that&#x27;s the index of refraction. Of the second medium are for red is 1.512 and in the index of refraction for violet, light into V is 1.53 So using that it wants us to find the angle of refraction for both cases. So we&#x27;re gonna use Snell&#x27;s Law, which says that, uh, in one times it&#x27;s rewrite this over here. So smells, Law says in one climbs the sign of the incident angle fatal. One is equal to in two times this sign of the angle of refraction. David too, which is what we&#x27;re trying to find in both cases. So for part, a solving for data to here we find that this is equal to the inverse sine which we right here is signed to the minus one of the ratio of in one times the sign of fate a one and then for the first case, this is the, uh, two that&#x27;s supposed to be They the one here. Since this is the first case, this is the case with the red light. So we call this into our for red. So taking the sign inverted the inverse sine of this ratio we find this is equal to 34 0.9 degrees. This could be boxed in. Is their solution for part a part B Reason the exact same thing smells law. So we&#x27;re gonna find the exact same relationship here. Except this time we&#x27;re using a different index of refraction. This time we&#x27;re using the index of refraction for the violet light. So it&#x27;s gonna be the inverse sine of in one times the sign of fatal one divided by the index of refraction for violet light, which we called into V plugging those values. In this expression, we find that this is equal to 34 0.5 degrees, so just slightly less in the red light weakened box it in is their solution for being

Problem

A horizontal incident beam consisting of white li…

Problem 84 Hard Difficulty

Answer

0.33 $\mathrm{deg}$

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