Question

calculate the refractive index of water with respect to glass and refractive index of glass with respect to water , if speed of light in water and glass is 2.2 × 10^8 m/s and 2 × 10^8 m/s respectively​

Answer 1

Answer:

c = Speed of light in air or vacuum = 3×108 m/s. μ = refractive index of the medium. So the refractive index of glass with respect to the water is 0.909. So this is the required answer.

Answer 2

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$\large\sf{ v_{w} = 2.2 \times {10}^{8} \: m/s} \\ \large \sf{ v_{g} = 2 \times {10}^{8}\: m/s}$

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$\sf \large \red{i)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies = \sf \large_w n_{g} = \dfrac{ v_{g}}{ v_{w}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies = \sf \large\dfrac{2 \: \times \cancel { {10}^{8} \: m/s }}{2.2 \: \times \cancel { {10}^{8} \: m/s }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies = \sf \large \cancel \dfrac{2}{2.2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies = \sf \large \dfrac{1}{1.1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies = \sf \large{0.909 \: \: (approximately)}$

The refractive index of water with respect to glass = 0.909 (approximately)

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$\sf \large \red{ii)} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies = \sf \large_g n_{w} = \dfrac{ v_{w}}{ v_{g}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies = \sf \large\dfrac{2.2 \: \times \cancel { {10}^{8} \: m/s }}{2 \: \times \cancel { {10}^{8} \: m/s }} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies = \sf \large \cancel \dfrac{2.2}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies = \sf \large {1.1} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

The refractive index of glass with respect to water = 1.1

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