Question:
The refractive index of water is $\frac{4}{3}$ and that of glass is $\frac{3}{2}$. The refractive index of glass with respect to water is
The refractive index of water is $\frac{4}{3}$ and that of glass is $\frac{3}{2}$. The refractive index of glass with respect to water is
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Remember: "Refractive index of X with respect to Y" always places the refractive index of X in the numerator and Y in the denominator.
Updated On: Jun 3, 2026
- $9/8$
- $8/9$
- $2/3$
- $3/4$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The relative refractive index of medium 2 with respect to medium 1 is defined as the ratio of the absolute refractive index of medium 2 to the absolute refractive index of medium 1: ${}^{1}\mu_{2} = \frac{\mu_2}{\mu_1}$.
Step 2: Meaning
Here, we are looking for the refractive index of glass ($g$) with respect to water ($w$), which mathematically corresponds to ${}^{w}\mu_{g} = \frac{\mu_g}{\mu_w}$.
Step 3: Analysis
We are given the absolute refractive values: $\mu_w = \frac{4}{3}$ and $\mu_g = \frac{3}{2}$. Substituting these values into the fraction yields: ${}^{w}\mu_{g} = \frac{3/2}{4/3} = \frac{3}{2} \times \frac{3}{4} = \frac{9}{8}$.
Step 4: Conclusion
Therefore, the relative refractive index of glass with respect to water is equal to $9/8$.
Final Answer: (A)
The relative refractive index of medium 2 with respect to medium 1 is defined as the ratio of the absolute refractive index of medium 2 to the absolute refractive index of medium 1: ${}^{1}\mu_{2} = \frac{\mu_2}{\mu_1}$.
Step 2: Meaning
Here, we are looking for the refractive index of glass ($g$) with respect to water ($w$), which mathematically corresponds to ${}^{w}\mu_{g} = \frac{\mu_g}{\mu_w}$.
Step 3: Analysis
We are given the absolute refractive values: $\mu_w = \frac{4}{3}$ and $\mu_g = \frac{3}{2}$. Substituting these values into the fraction yields: ${}^{w}\mu_{g} = \frac{3/2}{4/3} = \frac{3}{2} \times \frac{3}{4} = \frac{9}{8}$.
Step 4: Conclusion
Therefore, the relative refractive index of glass with respect to water is equal to $9/8$.
Final Answer: (A)
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