The figure shows a laser beam coming from the left, deflected by a 30-60-90 prism. What is the prism’s index of refraction?

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RizerMix · Accepted Answer

Step 1 The angle of refraction is as follows: ϕ=θ1+θ2 Here, angle of incidence is θ1 and angle between the refracted ray and the horizontal is θ2 Substitute 30∘ for θ1 and 19.6∘ for θ2 ϕ=30∘+19.6∘ =49.6∘ The equation for Snell’s law is as follows: n1sin⁡θ1=n2sin⁡ϕ Here, refractive index of air is n2 Rearrange: n1=n2sin⁡ϕsin⁡θ1 Step 2 The expression for refractive index of the prism is as follows: n1=n2sin⁡ϕsin⁡θ1 Substitute 49.6∘ for ϕ, 1.0 for n2, and 30∘ for θ1 n1=(1.0)sin⁡49.6∘sin⁡30∘ =1.52

Vasquez · Accepted Answer

Step 1 θ1+θ2=ϕ ϕ=30+19.6 =49.6∘ n1sin⁡θ=n2sin⁡θ2 n1=n2sin⁡θ2sin⁡θ =sin⁡(49.6)sin⁡(30) =1.52

alenahelenash · Accepted Answer

The refractive index of the area outside the prism is 1, this is the refractive index of a vacuum and is aproximatly equal to the refractive index of air (1.0008). You can find the angle of incidence by simple maths. Now if you form a triangle with the horizontal ray and the top of the prism you can say that the angle to the bottom right is 60 degrees, because of similar triangles. Now you need to find the angle between the ray and the normal which is perpendicular to the hypotenues of the prism Therefore: n2n1=n2=sin⁡θ1sin⁡θ2 That way: θ1=(σ2)+(ϕ2) θ1=30+15=45 degrees n2=sin⁡45sin⁡19.6=2.1

The figure shows a laser beam coming from the left,

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