As shown in Fig. E33.11

, a layer of water covers a slab of material X in a beaker. A ray of light traveling upward follows the path indicated. Using the information on the figure, find (b) the angle the light makes with the normal in the air.

Video transcript

Hi, everyone in this practice problem, we're being asked to determine the R, we will have a light ray in incident on a series of two solid slaps as shown in a figure. The first slap has an index of refraction of 1.53. And the second slap has an index of refraction of 1.47. The light emerges out of the second slip into the air forming an angle of data R with the normal to the surface. And we're being asked to determine what data R is by exploiting all of this data given in the problem statement. And in the figure in this case, we will also have data I listed or shown in the figure to be 42 degrees. So at slap two and, and er interface or in between the slap two and air interface, we will have to actually notice that N two is 1.47 then theta I is 42 degrees. And then we have N of air which is known to be one. And then lastly, we will have the, the R which is the one thing that we are interested to find So looking at the boundaries between slap two and er we can then apply snails law which will allow us to get the R. So according to Snell's law, N two multiplied by sine of theta, I will then equals to N of er multiplied by sine of theta R. This is looking at slap two and er boundaries, we wanna rearrange this equation in order for us to get sine of theta R, which will then allow us to get what theta R is. So in this case, sign of theta R will be equals to N two multiplied by sine of theta I divided by the end of err sign of the R will then equals to 1.47 multiplied by the sign of 42 degrees, which will then actually give us the sign of theta R to then equals to 0. 36. So next, we have to employ the in first of sin or sin to the power of negative one of 0.9836. Or in this case, we will employ a sin which is the in first of sin of 0.9836 to get theta R which will then give us theta R to be equals to 80 degrees. So theta R of 80 degrees will be the answer to this practice problem which will correspond to option D in our answer choices. So option D with theta R of 80 degrees will be the answer to this one. So that'll be it for this video. If you guys still have any sort of confusion, please make sure to check out our other lesson videos on similar topics and that'll be it for this one. Thank you.