Question

A light beam strikes a piece of glass at a 68.00 ∘incident angle. The beam contains two wavelengths, 450.0 nm and 700.0 nm, for which the index of refraction of the glass is 1.4831 and 1.4754, respectively.

Part A

What is the angle between the two refracted beams?

Express your answer using two significant figures.

θ700nm−θ450nm =

  ∘  

Answer 1

angle of incidence theta1 = 68 deg

refractive index of the glass is

n2 = 1.4831 (for 450 nm)

n2' = 1.4754 (for 700 nm)

by using snell's law,

n1*sin(theta1) = n2*sin(theta2)

for 450 nm,

n1*sin(theta1) = n2*sin(theta2)

1*sin(68) = 1.4831*sin(theta2)

sin(theta2) = sin(68)/1.4831

theta2 = 38.694 deg

and

for 700 nm,

n1*sin(theta1) = n2'*sin(theta2')

1*sin(68) = 1.4754*sin(theta2')

sin(theta2') = sin(68)/1.4754

theta2' = 38.934 degrees

angle between the refracted beam is

= (theta2') - (theta2)

= 0.234 deg.