Question

The index of refraction for a certain type of glass is 1.645 for blue light and 1.609 for red light. A beam of white light (one that contains all colors) enters a plate of glass from the air, nair≈1, at an incidence angle of 38.55∘. What is the absolute value of ????, the angle in the glass between blue and red parts of the refracted beams?

Answer 1

blue θ₂ = 22.26º

red θ₂ = 22.79º

Step-by-step explanation:

When a light beam passes from one material medium to another, it undergoes a deviation from the path, described by the law of refraction

n₁ sin θ₁ = n₂ sin θ₂

where n₁ and n₂ are the incident and transmitted media refractive indices and θ are the angles in the media

let's apply this equation to each wavelength

λ = blue

in this case n₁ = 1, n₂ = 1,645

sin θ₂ = n₁/ n₂ sin₂ θ₁

let's calculate

sin θ₂ = 1 / 1,645 sint 38.55

sin θ₂ = 0.37884

θ₂ = sin⁻¹ 0.37884

θ₂ = 22.26º

λ = red

n₂ = 1,609

sin θ₂ = 1 / 1,609 sin 38.55

sin θ₂ = 0.3873

θ₂ = sim⁻¹ 0.3873

θ₂ = 22.79º

the refracted rays are between these two angles