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Physics Question on Ray optics and optical instruments

A ray of light incident at an angle θ\theta on a refracting face of a prism emerges from the other face normally. If the angle of the prism is 5∘5^{\circ} and the prism is made of a material of refractive index 1.51.5, the angle of incidence is

A

7.5∘7.5^{\circ}

B

5∘5^{\circ}

C

15∘15^{\circ}

D

2.5∘2.5^{\circ}

Answer

7.5∘7.5^{\circ}

Explanation

Solution

According to the question, ray emerges from other surface of prism normally, ∴\therefore Angle of incidence at second face, r′=0∘r' = 0^{\circ} Now, r+r′=Ar+r' = A ⇒r=A−r′=5∘−0∘=5∘\Rightarrow r = A -r' = 5^{\circ} - 0^{\circ} = 5^{\circ} Using snell's law μ=sin isin r\mu = \frac{sin\,i}{sin\,r} or sin i=μsin r=1.5×sin5∘sin\,i = \mu sin\,r = 1.5 \times sin 5^{\circ} =0.131 = 0.131 ⇒θ=i=sin−1(0.131)\Rightarrow \theta = i = sin ^{-1} (0.131) =7.5∘ = 7.5^{\circ}