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(14 pts) Green light travels through water n = 1.333 and is incident on a prism with an apex angle of A = 65.008 and an index of refraction of n = 1.558 as shown be...

Question

(14 pts) Green light travels through water n = 1.333 and is incident on a prism with an apex angle of A = 65.008 and an index of refraction of n = 1.558 as shown below. The light ray is incident at an angle of 55.009 on the right face of the prism: a) Calculate the angle of refraction as it emerges from the left face: Carry angles to two places beyond the decimal in your calculations. Show all your work b) If the prism exhibits a standard dispersion characteristic, would the angle you calculated

(14 pts) Green light travels through water n = 1.333 and is incident on a prism with an apex angle of A = 65.008 and an index of refraction of n = 1.558 as shown below. The light ray is incident at an angle of 55.009 on the right face of the prism: a) Calculate the angle of refraction as it emerges from the left face: Carry angles to two places beyond the decimal in your calculations. Show all your work b) If the prism exhibits a standard dispersion characteristic, would the angle you calculated in a) be larger or smaller if the light were red instead of green? left face right face (6 pts) Carry three or four significant figures through all calculations. Show all your work A farsighted person has a near point of 65.0 cm and wishes to purchase lenses that will allow her to clearly see a computer screen that will be positioned 45.0 cm from her eyes a) Calculate the focal length of the lens that will serve this specific purpose_ b) What is the new far point distance for this person when wearing the corrective lens?



Answers

Angle of Deviation. The incident angle $\theta_{a}$ shown in Fig. 33.59 is chosen so that the light passes symmetrically through the prism, which has refractive index $n$ and apex angle $A$ . (a) Show that the angle of deviation $\delta$ the angle between the initial and final directions of the ray) is given by
$$
\sin \frac{A+\delta}{2}=n \sin \frac{A}{2}
$$
(When the light passes through symmetrically, as shown, the angle of deviation is a minimum. (b) Use the result of part (a) to find the angle of deviation for a ray of light passing symmetrically through a prism having three equal angles $\left(A=60.0^{\circ}\right)$ and $n=1.52 .$ (c) A certain glass has a refractive index of 1.61 for red light $(700 \mathrm{nm})$ and 1.66 for violet light $(400 \mathrm{nm}) .$ If both colors pass through symmetrically, as described in part (a), and if $A=60.0$ , find the difference between the angles of deviation for the two colors.

For about a week and right to smell the law that is in a sign sign. Sign their day that is equal to and B sign. Hey there, Toby. So I'm there, Toby, that be? Then we're given that a B is equal to a rover to over to Capitol A or two so we can ride. This snail's law is a sign sign that A that A is equal to a and B sign putting the value of Theta Bay, which is able to it was to hear. And then we know that A is equal to a plus. Too old for to also who are two is all over. It was too old. Then we can pluck the value of theta a year, and then our abode. The question becomes sign sign a plus tool for a plus to offer a plus two. Also over, too, is equal to so n and people right in on Lee. And then this becomes a sign. Sign a or two. They were, too, at each face off the prison, the angle off deviation Alpha is all far so for each face than for two faces. This is to all far physical to Delta. Then we can replace to also with the Delta in above equation. Then we can right equation above the Christian will become sign it plus dealt up. Delta or two is equal to Jim Sign Sign. There were two, and it is proved their design. Eight plus Delta or two is equal to end time. Signed a day or two in but be you're asked to find a delta for the given values or perfecting next. Then we can solve for a Delta from this equation. And once we sold for the Delta, that equation here we get here is two times. Sign off in worse. Sign off in worse into refractive index. Sign off, sign off air or do here or two. There were two. It's minus a minus D. So from a given data, then we can pluck those values and find the delta here so the Delta will become signing worse. Signing worse off refractive index is 1.52 five to and sign or 60 sign off 60 or two that is 30 30 and here we have singlets 30 60. Then we can just do the mats and sold. Then the delta you get? Here is 38 0.38 49 night. This is Sparta. Be for part C. But see, for the delta Red were dealt the red. So I kept all our for red. We will do the same procedure and just will replace here on end by 1.61 and angrily Sam is 60 degrees. Everything is saying except ah refractive index end. If I their place in a Bowie question, refractory next and by 1.61 and park this value in a bovie Christian here, then the delta red I get here is a 47 0.2 point to then for one minute for Delta War that we give it a week. We will do the same procedure, replacing in by 1.66 reflecting. Dex, If I plug this value up here again in this region, the security in then the delta V here I get here is 52 point 52.22 point two degrees. Then, from here, I can find ah delta off small delta. Oh, the angle. The difference off angle between red and wallet. Then I can just plug the values here which is 52 points for while it 52.2 minus. Ah for Red 47. I do. So the angle difference I get here is a five degrees end off the problem Think.

Learns to the geometric optics chapter in which we have a triangular prison. That is being used to reverse the that is being used to reverse the light beam. So for the part we have to determine will this work if prison is under the water which has refractive index and equals to one point triple three. Okay, So instead of inside the prison, the reflected beam will hit each leg of the prison at angle theta equals to 45 degrees. So for the prison water interface, the critical angle scientist to see it will be equals two critical angle of water to the critical angle of glass. So we get one point triple three divided by 1.5 to 0. So from here, critical angle courtesy comes out to be 61.28 degree. Okay, so the critical angle is 60.61 point to a degree, but the angle of incidence is 45 degrees. So we can say that total internal reflection will not occur. Total internal reflection will not occur. Okay, so this is the answer for this question and the most of the light will exit the prison so some light will get reflected, but the intensity will be look okay, This is the answer for the part. Now, moving to the part. B such prisons are used in preference to mirrors to bend the optical path in quality binoculars? Why? Okay, so for this question, the regions are caused. The quality mirrors require expensive reflecting coating and uh the next is quality that total internal reflection to reflect all the light. Okay, so these are the regions by the use of such prints. Okay.

Learns to the geometric optics chapter in which we have a triangular prison. That is being used to reverse the that is being used to reverse the light beam. So for the part we have to determine will this work if prison is under the water Which has refractive index and equals to 1. 3. Okay, So instead of inside the prison, the reflected beam will hit each leg of the prison at angle theta equals to 45 degrees. So for the prison water interface, the critical angle scientist to see it will be equals two critical angle of water to the critical angle of glass. So we get one point triple three divided by 1.5 to 0. So from here, critical angle courtesy comes out to be 61.28 degree. Okay, so the critical angle is 60.61 point to a degree, but the angle of incidence is 45 degrees. So we can say that total internal reflection will not occur. Total internal reflection will not occur. Okay, so this is the answer for this question and the most of the light will exit the prison so some light will get reflected, but the intensity will be look okay, This is the answer for the part. Now, moving to the part. B such prisons are used in preference to mirrors to bend the optical path in quality binoculars? Why? Okay, so for this question, the regions are caused. The quality mirrors require expensive reflecting coating and uh the next is quality that total internal reflection to reflect all the light. Okay, so these are the regions by the use of such prints. Okay.

In this question, being off light enters the sloping side off. I saw this wrangle triangle then, um, that's the you want. Oh, actually, parts in this question in part A. We want to find the angle of incidence published. Reflection on the vertical side is, uh, undergoes total internal reflection. Okay, so to labor some angles. Okay, So this is our angle of incidence. This is and go refraction. And then I'm going to call this data, see, for now and then this angle would be 135 degrees. Mhm. Yeah. So, um, we're going to use snails slow in the condition for total internal reflection to buy to solve for part a. Okay, so, uh, using. So this is the critical angle conditions for total internal reflection. So And we know that man is given to be 1.66 Mhm. Okay, So scientists see is to go to 1/1 0.66 And so did you see is calculated to be 37.0 degrees. Okay. And from the diagram, you know that data are plastic. Asi is 45 degrees, So data are if you go to 45 minus 37 degrees and you get 7.96 degrees. Okay. And from now it's law. Okay, we have scientist, I request to end. Sign there are. Okay, So, uh, side I is equal to 1.66 sign. 7.96 degrees. Right. It's just, uh this gives the I to be equal to 13 country degrees. Yeah. So this is the answer for party in part B. I went off. If the angle of incidents increases are, do we still get total internal reflection? Okay. Okay. So in part B, the answer is no. Okay, who's in? Uh, if data, I increase us. Okay. There there are increases in from sales law. Okay, then, did you see? Ah is, you know, uh, critical anger. So, uh, total internal reflection. Okay. Mhm. Yeah, because, uh, data are plus data, See, is 45 degree so data increases the labor data, See? Is going to be go smaller. Okay, So then then we are not going to get total internal reflection. Okay, Keeton Proxy, we want to find a minimum value off the total Internet. The minimum value off reflective index such that when we show very shy and horizontal bean. Ah, like that. Oh, yes. Grants. Yes. So, in part A, the being is not shining at horizontally. This is for policy. Okay, so, for a, uh, open in the beautiful party, this is what the being is coming. It looks like this. Okay, so this is for part A. Yeah, And then this game is for Patsy. Yeah. Sorry about that, Pete. So we want to find a minimum value of and such that when you have a horizontal beam and undergoes total internal reflection at the particular side of the prison. Okay, So wish horizontal bean he did. I would be 45 degrees so we can calculate are we're fact there the angle of refraction if using snows law. Okay, so we have sign whether I equals two and, uh, sign they are. Okay, we are supposed to find. And so and it's unknown. Okay, so, um, and we'll just be equal to, uh, sign 45 degrees. Bye bye. Sign there are so yeah given as such. And then from the total internal reflection condition. Yeah, you have sign. They see it goes through a wonderful and okay then from the diagram from diagram of both. Ah, they are us. They see becasue 45 degrees. Okay, so, um, is this what I'm going to do? I'm going to say okay. Scientists are is good, too. Sorry. 45 degrees minus status e. Okay. And then this is equal to one over n sign. 45 degrees. Okay. And, uh, this equation we expand, use the ah, you start trigonometry identity. So we have sai 45 degrees because I did a C minus co sign. 45 degrees site C is equal to when you were in Sorry. 45 degrees, right? Mm. 7. 45 degrees And cause I 45 degrees of the same at the same value. Right. Then, uh, you can just cancel them out. And because I didn't see minus one, they will end goes through when they will end. Okay. And then, uh, besides, jealousy is equal toe end. And this is, uh, one minus side square. They see square root. It goes to two over end and one minus one will end. Square is you goto for end square. So you're going to get, um, five. Who and square is equal to one and square it was five. Okay, so and it goes to 2.24 Okay, so this is the minimum. Ah, value of n you find it. Want to have total internal reflection on the vertical site off the prism refunding horizontal incident being okay, and that's all.


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