n 1 in other words and then looking up in the table <25.1>, we'll number out what this material might be. So we can number out what this angle α is using trigonometry based upon the dimensions given to us here and then knowing that this dotted black color line is a perpendicular to the interface, we deserve to say that Θ c climate is 90 minus this angle α that we'll find and also then understanding the crucial angle, we'll figure out what n 1 is. Okay! for this reason the crucial angle is 90 minus α for this reason let's figure out α. The tangent the α is the opposite foot of this ideal triangle divided by the adjacent leg so that's the train station tan then of 15.0 centimeters separated by 13.4 centimeters and that provides an edge of 48.22452 degrees, keeping lots of digits because this is an intermediary calculation. So i took the station tan that both sides here by the method to number out α. Okay! for this reason that's α and so then Θ c — the vital angle— is 90 minus that α and also that works out to 41.77548 degrees. And also then we usage this formula with the vital angle and also we have actually the first index the refraction the index of refraction the the very first material that the light is traveling with which is this orange liquid multiplied by sin of everything the vital angle is amounts to the index of refraction that the 2nd medium, i beg your pardon is wait in this case. So we resolve for n 1 by splitting both sides by sin Θ c and also then n 1 then is n 2 over sin Θ c. For this reason that's 1.000 split by sin that this edge that we found and also this works out to 1.501. And also when us look increase in table <25.1>, us look at liquids v an table of contents of refraction of 1.501... We uncover it here and the product must be Benzene. So this liquid is Benzene.">

You are watching: A ray of light emitted beneath the surface of an unknown liquid with air above it This is university Physics Answers v Shaun Dychko. Irradiate is being emitted by some light resource inside this liquid and light travels up and also hits this interface in between the liquid and also air and also then has complete internal reflection and also this is the smallest angle such that complete internal have fun occurs and that makes it the vital angle. So we have actually to number out what is the index of refraction the this material, what is n 1 in other words and then looking up in the table <25.1>, we"ll number out what this material can be. So we can number out what this angle α is using trigonometry based upon the dimensions offered to us here and also then discovering that this dotted black line is a perpendicular to the interface, we deserve to say the Θ c then is 90 minus this edge α that we"ll find and also then learning the an important angle, we"ll number out what n 1 is. Okay! therefore the vital angle is 90 minus α therefore let"s number out α. The tangent of α is the opposite foot of this appropriate triangle split by the surrounding leg so that"s the station tan climate of 15.0 centimeters separated by 13.4 centimeters and also that offers an angle of 48.22452 degrees, maintaining lots of digits because this is an intermediary calculation. So ns took the train station tan of both sides here by the way to figure out α. Okay! therefore that"s α and so then Θ c — the an essential angle— is 90 minus the α and that works out come 41.77548 degrees. And also then we usage this formula through the critical angle and we have actually the first index that refraction the table of contents of refraction the the very first material that the light is traveling v which is this orange liquid multiplied by sin of whatever the critical angle is amounts to the index of refraction the the 2nd medium, which is waiting in this case. Therefore we deal with for n 1 by splitting both sides by sin Θ c and then n 1 then is n 2 over sin Θ c. For this reason that"s 1.000 split by sin that this edge that we found and this functions out come 1.501. And when us look increase in table <25.1>, us look at liquids through an table of contents of refraction the 1.501... We find it here and the product must it is in Benzene. For this reason this fluid is Benzene.
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