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

• A. $9/8$
• B. $8/9$
• C. $2/3$
• D. $3/4$

Hint:

Remember: "Refractive index of X with respect to Y" always places the refractive index of X in the numerator and Y in the denominator.

Answer 1

The Correct Option is A

Step 1: Relative refractive index rule.
The index of medium 2 with respect to medium 1 is $^{1}\mu_{2} = \dfrac{\mu_{2}}{\mu_{1}}$.

Step 2: Set the right pair.
We want glass with respect to water, so $^{w}\mu_{g} = \dfrac{\mu_{g}}{\mu_{w}}$.

Step 3: Write the given values.
Water $\mu_{w} = \dfrac{4}{3}$ and glass $\mu_{g} = \dfrac{3}{2}$.

Step 4: Make the fraction.
\[ ^{w}\mu_{g} = \frac{3/2}{4/3} \]
Step 5: Flip and multiply.
\[ = \frac{3}{2}\times\frac{3}{4} = \frac{9}{8} \]
Step 6: State the answer.
So glass with respect to water is $\dfrac{9}{8}$, which is option 1.
\[ \boxed{^{w}\mu_{g} = \frac{9}{8}} \]