This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Right Ares, let's go. Question 3: If the fractional difference between the core and cladding refractive indices of the optical fibre is 0.0135 and numerical aperture NA is 0.2425, calculate the refractive indices of core and cladding materials. Step 1: List the given values and the relevant formulas. Given: Fractional difference, = 0.0135 Numerical Aperture, NA = 0.2425 Formulas: 1. Numerical Aperture: NA = n_1 sqrt(2) 2. Fractional difference: = (n_1 - n_2)/(n_1) Here, n_1 is the refractive index of the core and n_2 is the refractive index of the cladding. Step 2: Calculate the refractive index of the core (n_1). Using the numerical aperture formula: NA = n_1 sqrt(2) Rearrange to solve for n_1: n_1 = (NA)/(sqrt(2)) Substitute the given values: n_1 = (0.2425)/(sqrt(2 × 0.0135)) n_1 = (0.2425)/(sqrt(0.027)) n_1 = (0.2425)/(0.164316767) n_1 ≈ 1.4758 Step 3: Calculate the refractive index of the cladding (n_2). Using the fractional difference formula: = (n_1 - n_2)/(n_1) Rearrange to solve for n_2: n_1 = n_1 - n_2 n_2 = n_1 - n_1 Factor out n_1: n_2 = n_1 (1 - ) Substitute the calculated n_1 and the given : n_2 = 1.4758 (1 - 0.0135) n_2 = 1.4758 (0.9865) n_2 ≈ 1.4558 Step 4: State the final refractive indices. The refractive index of the core material is approximately 1.4758. The refractive index of the cladding material is approximately 1.4558. The refractive index of the core material is 1.4758 and the refractive index of the cladding material is 1.4558. What's next?