Question:A beam of light strikes a sheet of glass at an angle of 57.0deg.
with the...
Question
A beam of light strikes a sheet of glass at an angle of 57.0deg.
with the...
A beam of light strikes a sheet of glass at an angle of 57.0deg.
with the normal in air. You observe that red light makes an angle
of 38.1 degrees with the normal in the glass, while violet light
makes a 36.7 degree angle.
1.What are the indexes of refraction of this glass for these colors
of light?
2.What are the speeds of red and violet light in the glass?
The concepts required to solve the given question is Snell’s law and the sped in the different media.
Initially, calculate the refractive index for the red light and the violet light by using the Snell’s law equation. Later, calculate the speed of the red light. Finally, calculate the speed of the violet light.
Fundamentals
The expression for Snell’s law is as follows:
n2nr=sinθrsinθi
Here, nr is the refractive index of red light, n2 is the refractive index of air, θi is the angle of incidence, and θr is the angle of refraction.
The expression for Snell’s law is as follows:
n2nv=sinθrsinθi
Here, nv is the refractive index of red light, n2 is the refractive index of air, θi is the angle of incidence, and θr is the angle of refraction.
The expression for the velocity of the red light in as follows:
vr=nrc
Here, c is the speed of light.
The expression for the velocity of the red light in as follows:
vv=nvc
Here, c is the speed of light.
(1)
Substitute 57∘ for θi , 38.1∘ for θr , and 1.00 n2 in the equation n2nr=sinθrsinθi .
1.00nr=sin38.1∘sin57∘nr=0.6170.838=1.36
Substitute 57∘ for θi , 36.7∘ for θr , and 1.00 n2 in the equation n2nv=sinθrsinθi .
1.00nv=sin36.7∘sin57∘nv=0.5970.838=1.40
(2)
Substitute 3×108m/s for c and 1.36 for nr in the equation vr=nrc .
vr=1.363×108m/s=2.21×108m/s
Substitute 3×108m/s for c and 1.40 for nv in the equation vv=nvc .
vv=1.403×108m/s=2.14×108m/s
Ans: Part 1
The refractive index of red light is 1.36 and the refractive index of the violet light is 1.40.
Part 2
The speed of the red light is equal to 2.21×108m/s and the speed of the violet light is equal to 2.14×108m/s .