Question

Consider a beam of white light striking a face of an equilateral prism at an incident angle of Theta(1)= 50

Answer 1

For red light first.

Snell's Law...

n1sin(i) = n2sin(r)

1(sin 50) = 1.446(sin r)

r = 32 degrees (that is Theta 2)

Taking the geomentry of the problem, we need to go around the small triangle at the bottom to end up finding theta 3.

Follow along below

90 - r = 58 degrees (Since r = 32 and the normal is perpendicular to the surface

58 + 60 + x = 180 (the number of degrees in a triangle)

x = 62

Theta 3 = 90 - 62 (for the normal to the surface at the bottom)

Theta 3 = 28 degrees

Now apply Snells Law coming back out

1.446(sin 28) = 1(sin r)

r = 42.772 degrees

Now do the same for violet

n1sin(i) = n2sin(r)

1(sin 50) = 1.532(sin r)

r = 30 degrees (that is Theta 2)

Follow along

90 - 30 = 60 degrees

60 + 60 + x = 180

x = 60

Theta 3 = 90 - 60

Theta 3 = 30 degrees

Now apply Snells Law coming back out

1.532(sin 30) = 1(sin r)

r = 49.992 degrees

Finally subtract the two angles

49.992 - 42.772 = 7.22 degrees