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A light ray of wavelength 589 $\mathrm{nm}$ is incident at an angle $\theta$ on the top surface of a block of polystyrene as shown in Figure P35.60. (a) Find the maximum value of $\theta$ for which the refracted ray undergoes total internal reflection at the point $P$ located at the left vertical face of the block. What If? Repeat the calculation for the case in which the polystyrene block is immersed in (b) water and (c) carbon disulfide. Explain your answers.

a. This is not possible, i.e., there is no maximum value for the angle of incidence, and light always

undergoes total internal reflection on the left face of the block.

b. $=\left[30.3^{\circ}\right]$

(C) When polystyrene is immersed in carbon disulphide, there will be no total internal reflection,

as the refractive index of carbon disulphide is 1.628 , which is greater than that of polystyrene-

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Rutgers, The State University of New Jersey

Numerade Educator

Hope College

University of Winnipeg

let me draw the figure. So this is the surface, right? And, uh, light tree strikes this point Kangol cleaner. And then it, uh, refract towards the normal right? And let's say this angle East eater too. And from here, this light mingles in this direction. And let's see this angle. This angle used Tita three. Now, the single is teeter too. This one is. Feed it to him, right? Okay. No, let's do Kharkiv. No, me too. Party a well for the refracted rain toe Undergo a total internal reflection. Um, Peter three shown in the figure must be larger than the critical angle. So heated three must be greater than or equal to critical angle. And let's say this is acquitted Number one Well, we know the critical angle. Sign of critical angle equals and two divided by and one so critical angle equals sign, endorse into and two divided by in one. Right. And now, by substituting values critical angle, PTC is equal to sign in worse into 1.0 divided by one point for knowing so critical angle. T two c is equal to 42.0 40 to find 0 30 22.2 degrees. It's equal to 42 point two degrees. All right, now, let's substitute this value. Iniquity. Number one, Then we have Peter. Three is equal to or greater than 42 point two degrees. Let's say this is equity number to now from the geometry begin. See date Peter too. Bless Tito. Three eyes equal to 90 degrees. And Tito three is equal to 90 degrees minus teeter, too. Now, let's substitute this value in equipment to here. Well, then we have. Ah, uh, this equation becomes 90 minus leader to is credited than or equal to 42.2 degrees. And right there ah, solving for Peter to then pleaded to, is less than or equal to about 47 point eight degrees. 47 Going to eat? Uh, degrees, right? No. Let's use Snell's law. Snell's law says that in one time sign Frida one is equal to end two times. Sign Peter too, right? And substituting. Values 1.0 Time sign fate. A one is equal to one point for nine times signed, treated to and now scientists to sign. Pleaded to is equal to sign Peter one divided by one point for nine, Right? So Sign pleaded to is equal to one point. Uh ah. Sign Peter one divided by 1.49 And then by substituting, we get ah, sign Sign, Peter. One divided by one point for nine is less than or equal to 0.7 for one. What we consider it signed Fleet A one is equal to or less than, uh, 1.1 Zito. Well, this is true for any value for Peter one there for total internal reflection. Awkward for all values off, uh, leader. Now let us to part B. Well, for are police tiring, surrounded by water where the index of refraction off water is one point trey tree The critical angle ease feed. It sees equal to sign in worse into 1.333 divided by 1.49 which is equal to 63.5 degrees. Right. And since we know they feed, a three is greater than or equal to 6 to 3.5 degrees. Right, then, uh, we have a signed Tito to scientific Tory's, uh, less than or equal to zero point for for seven. And using Snell's law we have signed free to do well. Scientific. Ditto is equal to 0.8 95 dimes. Scientist. A one. Right. And from here, we can ride disease. Um, a sign, Peter one. Excuse me. Here, uh, became further right. This is See the point h 95 time sign. Pita one is less than or equal to see the point for for seven and sign feed alone is less than or equal to zero point for 47 divided by 0.895 which is equal to zero point for 99 And Peter one is less than or equal to signing. Worse off zero point for 99 which is equal to 30 0.0 degrees. So Peter want is equal to attorney. Fine. Zero degrees. Now for part C off the problem. Well, at the index of refraction for garbled isil, fight is 1.6 to 8. Which is larger thing for a police styling for Palestine in it is one point for nine. And we know the total internal reflection jokers is the light most from higher index medium into a lower index. Medium deal for the total internal reflection. Neighbor hawkers. So, uh, total internal reflection. Reflection? Never. Roker's never walkers