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Problem 59 Hard Difficulty

Figure P 22.59 shows the path of a beam of light through seyeral layers with different indices of refraction. (a) If $\theta_{1}=30.0^{\circ}$ , what is the angle $\theta_{2}$ of the emerging beam? (b) What must the incident angle $\theta_{1}$ be to have total internal reflection at the surface between the medium with $n=1.20$ and the medium with $n=1.00 ?$

Answer

a. $\begin{array}{l}{\text { Using Snell's law of refraction the index of refraction of water is obtained }} \\ {\text { from the slope of the plot. }} \\ {\qquad n \approx 1.35}\end{array}$
b. $\theta_{1} \geq 38.7^{\circ}$

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Video Transcript

here. Light travels through successive layers off different factor indexes off. So light, false trails from here to here. And this is making an angle off that one. And then it refracts into another medium. Then from there, it refracting too another medium. And then ah, right here. It's a reflection. This we call it that the one and this one is a that too, Um which is equal to think this one? That Ah too. And this one is angled that three which is a quote to in Lafitte a three year. And this is a call to angle data tree. So light comes in this direction. They're fact the necks of fast Medium is over 1.6 in second medium is 1.4 and effectiveness of 30 minutes 1.2 and the light exits into air. So what? Franklin It's is one here, and we can write for body A and one time sign that I want is a cult in two time sign that the two were and one is equal to 1.60 this first medium and and two is equal to one, and that one is equal to 30 degrees So this one is a 30 degrees for all successive layers from top to bottom. We get to the the relation that is 1.6 signed. 30. Is it called the 1.4 scientific that three. That is a quote from one point to scientific data for the physical. The one time sign made up, too. From here. Ah, scientific that three and sign So the state of four not signed rather fit the three years instead of four are a fraction in medium and musical to 1.4 and and physical to 1.2. Then we could write 1.6 old time science data sixties. A court one time scientists too, from here side that the two will be assigned a worse off. Is there a point? It excuse us 53.13 kidneys. That too, is emerging being mingled, which is cool too. 53.13 kidneys, but be the critical angle for the three, so there to see is equal to sign in. Worse off into driver in one where in one is greater than in two on one is equal to 1.202 physical one, then there to see will become signing worse off. Wondered why by 1.20 excuse us. 56.44 kidneys for successful layers. Then we can, right? When one time say it. Scientist one is 1.2 time signed 56.44 degrees, which is a good one, then this is a photo solid for theta one musical, signing yourself one the way by 1.6 Excuse us 38. 17 degrees. Thus, for the total in terra reflection to Walker, it's a surface with the surface between n musical the 1.2 and it is one. The angle one should be greater or equal to 38 on 70 weeks.

Wesleyan University
Top Physics 103 Educators
Elyse G.

Cornell University

LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Meghan M.

McMaster University