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Problem 46 Hard Difficulty

A ray of light is incident at an angle $30.0^{\circ}$ on a plane slab of flint glass surrounded by water. (a) Find the refraction angle. (b) Suppose the index of refraction of the surrounding medium can be adjusted, but the incident angle of the light remains the same. As the index of refraction of the medium approaches that of the glass, what happens to the refraction angle? (c) What happens to the refraction angle when the medium’s index of refraction exceeds that of the glass?

Answer

a.$ 17.5^{\circ}$

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Top Physics 103 Educators
Elyse G.

Cornell University

Andy C.

University of Michigan - Ann Arbor

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Aspen F.

University of Sheffield

Video Transcript

our question wants us to consider a ray of light going from water to Flint class. So the index of refraction of water in some W's 1.33 This ray of light hits with an angle of incident data one of 30 degrees, and the flint glass has a index of refraction of one place 66 So that's the situation we would consider for part a using Snell's law in one times the sign of state of one here is equal to in two. So the index refraction of the second medium type of the sign of data, too. Data to is what were asked to find for part A. And we're gonna consider the fact that in one is, uh, are in one here is water and are into here is glass. So then solving for fate a two. We find that it's equal to the inverse sine of the ratio of in one to end, too, which we said was water to glass. So in one whose water into his glass times the sign of fatal one, which was 30 degrees plugging those values into this expression we find a tutu is equal to 23 points, seven degrees for Part B. It says We'll consider. Um, consider the fact that we could have a changing medium. So now the glass is going to change mediums so that its index of refraction approaches the index of refraction of water. So in one would equal in two and Snell's law that we wrote for Part A or N W. So it would be in W times the sign of fatal one would be equal to N. W times. The sign of Zeta Tube, this is Thea are a big data to there instead of the one that's supposed to be 3 to 1 times in w sign of fated to. So that's what we're asked to consider where the index of refraction are both equal toe water. Well, if that's true, then signed data. One would equal sign dated, too, or theater one would just equal data to. So based on that logic, data one would equal fated to. So the index or the angle of refraction would be the angle of incident, and it would all be equal to 30 degrees. And that's our solution. Following that logic for Part B, Part C said now What if the medium that once was the flint glass uh, was changed? Where had an index of refraction that was greater than the index? Every fraction of water. So we would say now we're considering a, uh, excuse me, The index of refraction of the water, the surrounding water would be greater. It's asking us to consider the medium the surrounding medium, not the flint glass so would have to be greater than the glass and sub D. So according to our Snell's law equation, if, uh, the surrounding medium, which you were calling water is greater than glass, then we could say that according to this in one signed data, one which is equal to into signed data too, would indicate that data to would now have to be greater than fatal one. In order for that to remain true, it's Ah. Well, I guess it would be more correct to call it in someone here since her changing the medium, uh, to be something other than water. So this new medium call in someone is greater than in sub G. And in our equation here in sub two presents a G right, So their fourth data to would have to be greater than data one or the angle of refraction would be greater than the angle of incidence.

University of Kansas
Top Physics 103 Educators
Elyse G.

Cornell University

Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Aspen F.

University of Sheffield