Question

# Derive the expression for refractive index of the material of the prism in terms of angle of the prism and angle of minimum deviation.

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#### In the given diagram,OP is the incidence ray, which is making the angle i1 with normal, and QR is the angle of emergence, which is represented by i2. A is the prism angle and μ is the refractive index of the prism.Now, We know that,A=Prism angle, δ=Angle of deviation, i1=Angle of incidence, i2=Angle of emergent.In the case of minimum deviation,∠r1=∠r2=∠rA=∠r1+∠r2SO, A=∠r+∠r=∠2r∠r=A2Now, againA+δ=i1+i2 (∵ In the case of minimum deviationi1=i2=i and δ=δm)So, A+δm=i+i=2iNow, i=A+δm2Now, from snell's rule,μ=sin isin rμ=sinA+δm2sinA2 28
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