Refraction and Lenses Legacy Problem #6 Guided Solution

I have learned that a successful problem solver has learned to employ effective habits in approaching problems. Applying those habits here in this question involves reading the problem carefully and identifying the known and the unknown quantities, then using physics understanding and mathematical equations to plan out a strategy as to how to get from the known quantities to the unknown quantities. This question involves a refraction of light as it passes from air into oil, and the angle of incidence within the air is 36.1 degrees. I can call that theta 1 in the Snell�s law equation, theta 1 equals 36.1 degrees. And since this is the angle in air, I can call n1 1.00, since that is the index of refraction of air. Now on the other side of the Snell�s law equation, n1 times sine of theta 1 equals n2 times sine of theta 2, I don�t know anything. I don�t know n2, and I don�t know theta 2. In fact, they ask me to calculate the angle of refraction, so that would be the angle in oil. That would be theta 2, that�s my unknown quantity. The last bit of numerical information that�s given is the speed of light within that second medium, the oil. V in oil equals 2.27 times 10 to the 8th meters per second. So now I need to employ my other habits, which is plotting out a strategy by using physics concepts, conceptual understanding, and mathematical equations. I can think of two equations right now, and I�ve already talked about one of them, the Snell�s law equation, n1 times sine of theta 1 equals n2 times sine of theta 2. But the other equation is the equation which relates the speed of light within a material to the speed of light within a vacuum, and the index of refraction. That equation goes something like this, n, the index of refraction, is equal to c, the speed of light within a vacuum, divided by v, the speed of light within that material. So if I want to find the n of oil, I can do it as long as I know the speed of oil. And once I learn the n of oil, I can plug that into my Snell�s law equation, because that would be n2, and I can solve for theta 2, the angle of refraction within the oil. So employing this strategy goes something like this, n2 is equal to c divided by v, where the c is 2.998 times 10 to the 8th, and the v equal 2.27 times 10 to the 8th. When I do that, I get 1.3207. Now I can plug 1.3207 into Snell�s law equation for n2. I would have now, 1.00 times the sine of 36.1 degrees is equal to 1.3207 times the sine of theta 2. Getting sine of theta 2 by itself on the same side of the equation involves dividing each side of the equation by 1.3207. That gives me sine of theta 2 equal 0.44612. To find theta 2, I need to ask my calculator what angle has a sine value of 0.44612. That involves having, on at least my TI graphing calculators, pressing the second sine button, that�s two buttons, second and sine, that�s the inverse sine, and then entering 0.44612. Then when I press return, I�m going to get the answer of 26.495 degrees. Using my scientific calculators, I probably have to first have 0.44612 entered into the calculator panel, and then I press second sine, and it should give me the same value of 26.495, and I can round that to three significant digits.