Let
ni= the index of refraction for the material with incident light,
nr= the index of refraction for the material with refracted light,
θi= the angle of incidence, and
θr= the angle of refraction.
Law of refraction (Shell's Law)
nisinθi=nrsinθr Given na=1,ng=1.550,nm=1.329
a)
From air to glass
nasinθ1=ngsinθ21⋅sin41.3°=1.550⋅sinθ2θ2=arcsin(1.550sin41.3°)≈25.2° From glass to methanol
ngsinθ2=nmsinθ31.550⋅sin25.2°=1.329⋅sinθ3θ3=arcsin(1.3291.550⋅sin25.2°)≈29.8° b)
From glass to unknown liquid
ngsinθ2=nusinθu=>nu=sinθusinθ2⋅ngnu=sin20.2°sin25.2°⋅1.550≈1.911
The refractive index of the unknown liquid is 1.911
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