Question

A beam of light strikes a sheet of glass at an angle of 58.0 ∘∘ with the normal in air. You observe that red light makes an angle of 37.7 ∘∘ with the normal in the glass, while violet light makes a 36.7 ∘∘ angle. Part A What are the indexes of refraction of this glass for these colors of light? Answer in the order indicated. Separate your answers with a comma. nred,nvioletnred,nviolet = nothing SubmitRequest Answer Part B What are the speeds of red and violet light in the glass? Answer in the order indicated. Separate your answers with a comma. vred,vvioletvred,vviolet = nothing m/sm/s SubmitRequest Answer Provide Feedback

Answer 1

a) The index of refraction for the red light is 1.39 and the index for the violet light is 1.42

b) The speed of the red light is 2.15x10⁸m/s and the speed of the violet light is 2.11x10⁸m/s

Step-by-step explanation:

a) Using Snells law:

`n_(1) sin(i)=n_(2) sin(r)n_(2) =(n_(1)sin(i) )/(sin(r))`

For red light:

`n_(1) sin(i)=n_(2) sin(r)n_(2) =(n_(1)sin(i) )/(sin(r))=(1*sin58)/(sin37.7) =1.39`

For violet light:

`n_(1) sin(i)=n_(2) sin(r)n_(2) =(n_(1)sin(i) )/(sin(r))=(1*sin58)/(sin36.7) =1.42`

b) The speed for the red light is:

`v=(c)/(n)`

Where c is the speed of the light

`v=(3x10^(8) )/(1.39) =2.15x10^(8) m/s`

The speed for the violet light is:

`v=(3x10^(8) )/(1.42) =2.11x10^(8) m/s`

Answer 2

Step-by-step explanation:

using Snell's law of refraction

n₁ sinθ₁ = n₂ sinθ₂

where n₁ = the indexes of refraction of the material with incident light

n₂ = the indexes of refraction of the material with refracted light

θ₁ = angle of incidence and θ₂ = angle of refraction

for red light

n₁ sinθ₁ = n₂ sinθ₂

1 × sin 58 = n₂ sin37.7

n₂ = ( 1 × sin 58) / sin 37.7° = 1.387 for red light

for violet light

n₁ sinθ₁ = n₂ sinθ₂

1 × sin 58 = n₂ sin36.7

n₂ = ( sin 58 ) / sin36.7 = 1.419 for violet light

the speed of red light can be calculated with formula below

n = c / v where c is the speed of light = 3 × 10 ⁸ m/s and v is the speed of the red light

v = c / v = (3 × 10 ⁸ ) / 1.387 = 2.163 ×10 ⁸ m/s

for violet light

v = ( 3 × 10 ⁸) / 1.419 = 2.11 × 10 ⁸ m/s