# SOLVED:In Figure 23.12, a coin is right up against the far edge of the mug. In picture (a) the coin is just hidden from view and in picture (b) we can almost see the whole coin. If the mug is 6.5 \mat

### Video Transcript

Okay, I ‘ve got a grating sketch of this situation here, and I ‘ll explain my sketch. We ‘ve got the mud that is 8.9 centimeters improbable. And when that mug, um, has nothing in it, the coin is out of view. Um, and we use that information to get this straight occupation from the I don here to point B for the width of the countenance, which is 6.5 centimeters. And when that mug is filled with water, the rays are the view that we have is refracted due to the index of deflection with water and how it bends the race. So we ‘re going to use that information in a little bite of geometry in order to figure out the diameter of this mint that comes into scene in the mug is filled with body of water. So they get started. We want to figure out this duration correct here of the senior high school pot news in order to use um and then we use that data holy order to figure out this lean of reflection hera. This slant of reflection is adequate to this fish down here, and they ‘re just complementary color angles or congruous ankles. So we ‘ll use the tha k ‘s theorem to solve for the length of a B. The dragon Pythagorean serum is one side squared plus, the other side squared was equal to the high pot New squared. And we can rearrange this to solve for the duration of the high gear pot news square ancestor of a C squared plus C b squared. And then when I substitute in my values 8.9 squared plus 6.5 squared and you square root all of that you get 11.1 centimeters. So that is the length of our high pot news. immediately we can use that data. I want you to recall something from way back Wing called so Kyoto. Uh, so Kyoto, uh, looks like this. It helps us remember how we can use gestural co sine and tangent. So the sign of the opposite yoke divided by the length of the ballyhoo oddness would tell us this lean. So that ‘s what we do next. The sign of this lean is equal to the duration of CB divided by the length of a B. So we take, um, 6.5, divided by 11.1 That gives a 0.5 nine, and we do n’t even have to solve for good this angle because we can substitute this in two Snell ‘s law. Whenever we do that, which is adjacent. therefore smells all we ‘re going to use in order to figure out we know now the the value for sign, angle of refract observation. It ‘s now we ‘re going to figure out the lean of incidents. So we set up in one sign data angle of incidents. And keep in beware that are medium for this lean of incidence is water. sol in one is going to be the slant of index of deflection for urine, which is 1.33 and then when we see the visualize, it ‘s in the tune. So the into is the index of refraction for air we signed data are, and we ‘re going to rearrange this to solve for that angle of incidents. So we get the inverse sign of into sign data are divided by in one when I substitute my values into is 1.0 sign data are remember is 0.59 and then we divide all of that by 1.33 which is the index of deflection for water and then gives us the respect of 26 0.33 degrees. so now we know this slant right here, and that is an angle for the triangle a C D. In order to figure out the diameter of this coin, we need to figure out the distance of C. D. So again we ‘re going. We ‘re going to use geometry. We will use hand data. I soto a tells us opposite over adjacent deoxycytidine monophosphate D, divided by a scene when we saw for fair certificate of deposit, we get certificate of deposit equal to a C Times tan data I when I substitute in my values 8.9 centimeters time 10 26.33 And that gives me a value of 4.4 centimeters and we ‘re about done. now that we know this length up here, which is 4.4, we precisely need to subtract that from 6.5. So the diameter of the mint is 6.5 minus 4.4, equitable peer to 2.1 centimeters

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