Question

A beam of light containing red (660 nm) and violet (410 nm) wavelengths travels from air, through a flat piece of crown glass 1.38 cm thick, and then back to air.

(a) If the beam has an angle of incidence of 20.2° in air, determine the angle at which the two colors of light emerge from the crown glass. The index of refraction respectively for red and violet light in crown glass is 1.512 and 1.530. (Enter a number to three decimal places.)

red	°
violet	°

(b) Determine the distance separating the red and violet light as it emerges from the glass.
=

Answer 1

lambda_red=660nm

lambda_violet=410nm

thickness of the crown glass, t=1.38 cm

a)

angle of incidence, theta=20.2 degrees

here,

angle of emerging is also same as angle of incidence,

for both red and violet light, angle of emerging = 20.2 degrees

b)

by using Snell's law,

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

for the red light,

1*sin(20.2)=1.512*sin(theta2)

===> theta2=13.2 degrees

distance travelled by the red light, x1=t*tan(theta2)

x1=1.38*tan(13.2)

x1=0.324 cm

and

for the voilet light,

1*sin(20.2)=1.53*sin(theta2)

===> theta2=13.043 degrees

distance travelled by the voilet light, x2=t*tan(theta2)

x2=1.38*tan(13.043)

x2=0.319 cm

the separating distnace between the red and voilet light as it emerges,

d=x1-x2

d=0.324 - 0.319

d=5*10^-3 cm