The following question is part of review for refraction in an algebra-based phys
ID: 1553289 • Letter: T
Question
The following question is part of review for refraction in an algebra-based physics course. It would be great in helping my understanding if the work was shown. Thanks!
The following figure shows the path of a beam of light through several layers with different indices of refraction. a) Determine the angle 04 in terms of 01,n1,n2,n3 and/or n4. b) Determine the angle 01 that will result in the total reflection at the surface between the medium n2 and n3? c) Work out the problem a) with 0 30.00, nl 1.60, n2 1.40, n3 1.20, n4 1.00 d) Work out the problem b) with n1 1.60, n2 1.40, n3 1.20, n4 1.000 n1 n2 naExplanation / Answer
Applying snell's law,
ni sin(i) = nr sin(r)
n1 sin(theta1) = n4 sin(theta4)
sin(theta4) = n1 sin(theta1) / n4
theta4 = sin^-1 [ n1 sin(theta1) / n4]
(B) TIR at surafce between n2 and n3.
n2 sin(theta2) = n3 sin90
sin(theta2) = n3 / n2
now applying snell's law for ray going from surface n1 to n2.
n1 sin(theta1) = n2 sin(theta2)
n1 sin(theta1) = n2 (n3 / n2) = n3
theta1 = sin^-1(n3 / n1)
(C) theta4 = sin^-1 [ n1 sin(theta1) / n4]
sin(30) = 0.5
theta4 = sin^-1[ 1.60 x 0.5 / 1] = sin^-1(0.8)
theta4 = 53 deg
(D) theta1 = sin^-1(1.20 / 1.60) = sin^-1(3/4)
theta1 = 48.6 deg
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