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Homework Help: Snell's Law HELP TEST TOMMOROW

  1. Jan 28, 2007 #1
    Snell's Law HELP!! TEST TOMMOROW!!!

    1. The problem statement, all variables and given/known data

    Hi, I have a problem with Snell's Law...i understand that it is:
    n1(sin)theta1 = n2(sin)theta2

    but for the test, we need to know how to manipulate the problem to find the angle of refraction...i will have a calculator to plug thing in but i just don't understand how to!!! Apparently after you find one thing you need to use an inverse sin (sin-1) or something...PLEASE HELP!!!

    An example problem for this is:
    A Beam of light passes from glass (n=1.51) to an unknown medium X (nX=?).
    If the angle of incidence is 40 and the angle of refraction is 29 then the index of refraction of the unknown medium is closest to:
    a)1.17, b)1.38, c)1.63, d)1.83 or e)2.00

    Followed by: The beam of light exists medium X and enters air. If it has an incident angle of 29 at the X-Air boundary, find the angle of refranction in the air?



    3. The attempt at a solution
    for example my notes say: Nw(sin)theta W = Na(sin)theata A
    w=water=1.333
    a=air=1
    1.333(sin)theta W=1 x sin(37)(angle of incidence)
    sin thetaW=sin(37)/1.333
    Theta W= (sin -1)/(inverse sin) [sin(37)/1.333]

    WHY IS IT GO FROM SIN(theta W) TO INVERSE SIN!?

    I Know there is a lot fo questions and info here...these are questoins from a quiz i did and i did very poorly...my test is tommorow and help would be greatly appretiated THANKS SOOO MUCH!!
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 28, 2007 #2

    hage567

    User Avatar
    Homework Helper

    To explain the inverse trig function part:

    Starting with this line of your example:

    sin(theta_w)=(sin37/1.333)

    The sin^-1 (or inverse sin, also called arcsin) is just a function that you use to "undo" the sin(theta_w) to get just theta_w. You apply it to both sides of your equation like you would anything else when trying to isolate a variable. So you would have

    sin^-1{sin(theta_w)} = sin^-1{sin37/1.333}

    the left side then becomes just theta_w, and by calculating the right side you get the angle of refraction.
     
  4. Jan 29, 2007 #3
    ooooo thanks so much....the test was still REALLY hard but what can you do...thanks a ton i appreatiate it
     
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