A laser beam strikes one end of a slab of material, as in Figure P22.56. The index of refraction of the slab is 1.48. Determine the number of internal reflections of the beam before it emerges from the opposite end of the slab.
we're asked to look at figure p 22.56 for this, um, where light enters a slab with an index of refraction in of 1.58 and it gives you some information here. I call the length of this lab l for 42 centimeters. The thickness of the slab is estimates 420.31 centimeters. Okay, and enters at an angle of 50 degrees. And it wants us to figure out how many times the internal reflection will occur. What's the number of total internal reflections before emerges at the opposite end? Okay, so the first thing we need to do for this is find the second, the index every fraction, or they did too. We could do that using smells law. Well, since it's coming from air with an index of refraction of one, we can just ignore that. So we have signed fatal one is equal to in science data, too. Okay, we can solve for theta to hear when we find that it's equal to the inverse sine, uh, just signed to the minus one of the ratio of ah signed data one divided by in. So we find that data to here is equal to 31.2 degrees. That will become important here in a second. Okay, so, um, looking now? Ah, at the figure just from refraction occurs at X equals D in the second at X equals three D and hints for in number of times. Right. So the total distance it travels l here than the equation is equal to, uh, two times the number of internal reflections minus one times the, uh, distance in between each one. D Okay, Well, D here is equal to 1/2 the thickness, which is s so this would be 1/2 s, then, using just a simple trigonometry divided by the tangent of fate. A two. Okay, so then that distance then is equal to 0.256 centimeters. So we know l we know d we consult for in so doing that plugging that into that equation for Ellen d we find that, uh, in is equal to 1/2 l divided by d plus one. Okay, so plugging in the values for l and D in this expression, we find that in is equal to 82.5, but you can't complete half of a cycle, so we'll just call that 82 that could be boxed in as their solution to the question.