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Total Internal Reflection

In Fig. 33-60, light enters a $90^{\circ}$ triangular prism at point $P$ with incident angle $\theta,$ and then some of it refracts at point $Q$ with an angle of refraction of $90^{\circ} .$ (a) What is the index of refraction of the prism in terms of $\theta ?$ (b) What, numerically, is the maximum value that the index of refraction can have? Does light emerge at $Q$ if the incident angle at $P$ is (c) increased slightly and (d) decreased slightly?

(a) $n=\sqrt{\sin ^{2}(\theta)+1}$

(b) $n_{\max }=1.41$

(c) light leaves the second surface and emerges into the air

(d) so all the light is reflected at $Q$

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Oh, this question. We have light entering the prison at point B, and we've incidents angle off here in the in this diagram we call to you know what and then some of it reflected point Q. With angle for a fraction off 90 degrees. So this point Q. And this is the angle of refraction here. First, they want to know where is the index of refraction victims. Off the instance is the single, So the other one is incident angle didn't do this, then go over fracture at the first surface. So we have the information that we have here is the other one is the incidents to enter, too, is the refraction point Pete painted. Three. Is the incidence at Point Cube? Yes, there's a P and therefore is nine degrees Is the refraction appoint Q. So we have this information, and the more of this the right the left. So now we can use the law off refraction. So we we have lost refraction on cue and at one Q. You. Thank you. So we have in the second surface we have and sign off till three is equal to sign off before we are assuming that outside air. So this is and Tito, because toe and way can relate the interior angles here because there are complimentary. So we have that make that three is equal to 90 degrees My understated too. So we can use this in this equation here. So we have and sign off 90 degrees My understated too. Is you going too well? Is this it could tow and cross sign off here too, that we can also ride this eyes and square old off one minus sign square theater too. Now we we are applying their low offer a fracture. I appoint you be here but I have to do this. But point B, we have sign off. Pita one is equal toe end sign of theater too. So this gives us sign needed to is you control So off the yellow one, By the way I am And we can then use this in this equation here. So we have the equation and square root of one minus sign square off there. Two. Is it going to work? This is the equation that we got from the refraction. But Cube and we can use now their information from refraction and beautiful, too, right in terms of the instance handle. So this iss, um square root off one minus signs square off terror one divided by end square It was one. And we can't square both sides and so forth and so and is equal to square root of one plus science. We're off 01 We achieved what we want. Do we want to write the index refraction terms off here now for part B, they want to know where is the maximum value that the index of refraction can rest has And if light of mirrors that cue if the incidents and go at B is increase in the crease, so the maximum value is when sign It's great isn't good to one. So let's and next is when science squares you could work. This is equal to squared off That is one point for you one. So this is the maximum refraction or B for a C. They want to know Ah, if lighting millions if we increase the angle a little bit so for a little value off and if the angle of incidence at the first surface is greater than their leader one. So you answer this great off the other one, the M o for faction. There is greater than teacher, too. And the blow off instance at the separate face is last in 2 to 3. This means that the quick Oh, and go for the total, this means bent the final angle in this office here own territory. So this means that in the three prime will be less then two or three. And because of that, you be less then the critical angle. And this means that ah like to leave because we have the bangle. It is more than the kids going go so we can let pass, like passed through the situation's difference different If we have, uh, I angle off, it's this smaller then Tito one, because now the science, the the the quality will change. So this means that tentative prime will be greater than 2 to 3. And this means that did that. Three prime will be greater than the Crisco angle and because it's greater than the Crisco and go all light will be reflected. So here, light process and oh reflected

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