Question

The Refractive Index (RI) of the glass and water is 1.5 and 1.33 respectively. If the glass is immersed in water, its refractive index is

• A. 0.89
• B. 1.13
• C. 1.99
• D. 2.83

Hint:

When a material is placed in a medium other than vacuum/air, its effective refractive index relative to the surrounding medium is always less than its absolute refractive index because $n_{\text{medium}} > 1$.
Here, $^{w}n_{g} = \frac{1.5}{1.33} = 1.13$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We are given the absolute refractive indices of glass ($n_g = 1.5$) and water ($n_w = 1.33$). We need to find the relative refractive index of glass when it is immersed in water.

Step 2: Key Formula or Approach:
The relative refractive index of medium 2 with respect to medium 1 is defined as:
\[ ^{1}n_{2} = \frac{n_2}{n_1} \] When glass (medium 2) is immersed in water (medium 1), its relative refractive index with respect to water ($^{w}n_{g}$) is:
\[ ^{w}n_{g} = \frac{n_g}{n_w} \]

Step 3: Detailed Explanation:
• Express the absolute refractive index of glass: $n_g = 1.5$.

• Express the absolute refractive index of water: $n_w = 1.33 \approx \frac{4}{3}$.

• Calculate the relative refractive index:
\[ ^{w}n_{g} = \frac{1.5}{1.33} \]
• Performing the division:
\[ ^{w}n_{g} \approx \frac{1.5}{4/3} = \frac{4.5}{4} = 1.125 \]
• Rounding to two decimal places gives $1.13$.

Step 4: Final Answer:
The relative refractive index of the glass when immersed in water is approximately 1.13.