The refractive index (n) of a material is defined as the ratio of the speed of light in a vacuum © to the speed of light in that material (v). Therefore, we can calculate the speed of light in material X for red light as v_red = c / n_red = c / 1.80. Similarly, the speed of light in material X for blue light can be calculated as v_blue = c / n_blue, where n_blue is the refractive index for blue light in material X.
We are given that blue light travels 5 × 10⁶ m/s slower than red light in this material. Therefore, we can write:
v_blue = v_red - 5 × 10⁶ m/s
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Substituting the expressions for v_red and v_blue, we get:
c / n_blue = c / 1.80 - 5 × 10⁶ m/s
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Solving for n_blue, we get:
n_blue = c / (c / 1.80 - 5 × 10⁶ m/s) ≈ 1.81
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Therefore, the refractive index for blue light in material X is approximately 1.81 123.