Physics

Physics

Problem

For a prism of prism angle θ=60∘\theta = 60^\circ , the refractive indices of the left half and the right half are, respectively, n1n_1 and n2n_2 (n2≥n1n_2 \ge n_1) as shown in the figure. The angle of incidence ii is chosen such that the incident light rays will have minimum deviation if n1=n2=n=1.5n_1 = n_2 = n = 1.5 . For the case of unequal refractive indices, n1=nn_1 = n and n2=n+Δnn_2 = n + \Delta n (where Δn≪n\Delta n \ll n), the angle of emergence e=i+Δee = i + \Delta e . Which of the following statement(s) is(are) correct? ![Diagram of a prism with apex angle theta. The prism is divided into two halves by a vertical dashed line. The left half has refractive index n_1 and the right half has refractive index n_2. An incident ray is shown approaching the left face, making an angle i with the normal.](https://storage.googleapis.com/diraq-contents/homework-question-parsing/marker/20260106T182719Z/b0e26d76e64947c18b4c861dc7fc690e/935eed7aa61f7777f62cfc032e11bee9_img.jpg) (A) The value of Δe\Delta e (in radians) is greater than that of Δn\Delta n (B) Δe\Delta e is proportional to Δn\Delta n (C) Δe\Delta e lies between 2.0 and 3.0 milliradians, if Δn=2.8×10−3\Delta n = 2.8 \times 10^{-3} (D) Δe\Delta e lies between 1.0 and 1.6 milliradians, if Δn=2.8×10−3\Delta n = 2.8 \times 10^{-3}

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