A beam of light containing red (660 nm) and violet (410 nm) wavelengths travels

Question

A beam of light containing red (660 nm) and violet (410 nm) wavelengths travels from air, through a flat piece of crown glass 2.10 cm thick, and then back to air.

(a) If the beam has an angle of incidence of 17.0° 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.)

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

Explanation / Answer

using snell's law:

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

where n1, n2 are refractive index for medium 1 and medium 2

theta1=angle of incidence at medium 1

theta2=angle of refraction at medium 2

for red light:

refraction from air to crown glass:

n1=1

n2=1.512

theta1=17 degrees

then theta2=arcsin(1*sin(17)/1.512)=11.15 degrees

now, for refraction from crown glass to air:

n1=1.512

n2=1

theta1=11.15 degrees

then theta2=arcsin(1.512*sin(11.15)/1)=17 degree

so red light will emerge at an angle of 17 degrees.

distance from incidence point to the point where red light will emerge=thickness*tan(angle f refraction)

=2.1*tan(11.15)=0.41391 cm

for violet light:

refraction from air to crown glass:

n1=1

n2=1.53

theta1=17 degrees

then theta2=arcsin(1*sin(17)/1.53)=11.017 degrees

now, for refraction from crown glass to air:

n1=1.53

n2=1

theta1=11.017 degrees

then theta2=arcsin(1.53*sin(11.017)/1)=17 degree

so red light will emerge at an angle of 17 degrees.

distance from incidence point to the point where red light will emerge=thickness*tan(angle f refraction)

=2.1*tan(11.017)=0.40885 cm

answers are:

part 1:

red light will emerge at angle of 17 degrees

violet light will emerge at angle of 17 degrees

part 2:

distance between the emerging points=0.41391-0.40885=0.00506 cm

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