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The index of refraction for violet light in silica flint glass is 1.66, and that for red light is 1.62. What is the angular spread (in degrees) of visible light passing through a prism of apex angle 60.0° if the angle of incidence is 54.0°? See figure below. A triangular prism is shown. A ray of visible light moves up and to the right and is incident on the left edge of the prism. Inside the prism a rainbow of colors spreads out from the incident ray and in order from top to bottom they are red, orange, yellow, green, blue and violet. Once the rainbow leaves the prism, it continues to move down and to the right but all the colors are at slopes which are steeper than they were within the material. The rainbow is then projected onto a screen. The angular spread between the red and violet colors is indicated. A dashed line extends from the incident ray on the left to the right and the angle that this line makes with the red light ray is labeled Deviation of red light. ° (b) What If? What is the maximum angular spread (in degrees) for white light passing through this prism?

Respuesta :

Finti

Answer:

4.2°

Explanation:

Snell’s law gives:-

n₁ sin θ₁ = n₂ sin θ₂

Given, θ₁ = 54.0°

For the refraction of violet light ( n = 1.66 ) from air to glass:

( 1.00 ) sin 54.0° = ( 1.66 ) sin θ₂₁

sin θ₂₁ = ( 1.00 / 1.66 ) sin 54.0° = 29.2

For the refraction of violet light from glass to air …  

n₂ sin θ₂ = n₃ sin θ₃₁

θ₂ = 60 -29.2 = 30.8

n₂ = 1.66

n₃ = 1

sin θ₃₁ = ( n₂ / n₃ ) sin θ₂ = n₂ sin θ₂₂ = ( 1.66 ) sin 30.8°  

θ₃₁ = sin ⁻ ¹ [ ( 1.66 ) sin 30.8° ] = 58.2°

For the refraction of red light ( n = 1.62 ) from air to glass

( 1.000 ) sin 54° = ( 1.62 ) sin θ₂

sin θ₂ = ( 1.000 / 1.62 ) sin 54°  

θ₂ = sin ⁻ ¹ [ ( 1.000 / 1.62 ) sin 54° ] = 29.95986° = 30.0°

For the refraction of red light from glass to air

n₂ sin θ₂ = n₃ sin θ₃₂

n₂ = 1.62 , θ₂ = 30° , n₃ = 1.000 …  

sin θ₃₂ = ( n₂ / n₃ ) sin θ₂ = n₂ sin θ₂ = ( 1.62 ) sin 30°

θ₃₂ = sin ⁻ ¹ [ ( 1.62 ) sin 30° ] = 54°

Angular spread =   γ = θ₃₁ - θ₃₂ = 4.2°

The angular spread in degrees of visible light passing through a prism of ap ex angle 60.0° if the angle of incidence is 54.0° is; 4.1°

What is the angular spread?

For incoming rays, sin sin θ₂ = (sin θ₁)/n

Thus;

(θ₂)_violet = sin⁻¹ ((sin 54)/1.66)

(θ₂)_violet = 29.17°

(θ₂)_red = sin⁻¹ ((sin 54)/1.62)

(θ₂)_red = 29.96°

For the outgoing ray;

(90 - θ₂) + (90 - θ₃) + 60° = 180°

Also, θ₃ = 60 - θ₂ and sin θ₄ = n sin θ₃

(θ₄)_violet = sin⁻¹ (1.66 * sin 30.83))

(θ₄)_violet = 58.29°

θ₄)_red = sin⁻¹ (1.62 * sin 30.04))

(θ₄)_red = 54.19°

The angular dispersion is the difference and so;

Angular dispersion = (θ₄)_violet - (θ₄)_red

Angular dispersion = 58.29° - 54.19°

Angular Dispersion = 4.1°

Read more about angular dispersion at; https://brainly.com/question/13972198