Question

The refractive indices of flint glass and alcohol are 1.65 and 1.36 respectively with respect to air. What is refractive index of flint glass with respect to alcohol ?

• A. 1.32
• B. 1.42
• C. 1.21
• D. 1.72

Hint:

Refractive index of medium 'A' with respect to medium 'B' (\(n_{AB}\)) is: \[ n_{AB} = \frac{\text{Absolute refractive index of A (w.r.t. air/vacuum)}}{\text{Absolute refractive index of B (w.r.t. air/vacuum)}} \] Here, we want refractive index of flint glass (let's call it G) w.r.t. alcohol (let's call it L). So, \(n_{GL} = \frac{n_G (\text{w.r.t. air})}{n_L (\text{w.r.t. air})}\). Given: \(n_G = 1.65\) (flint glass w.r.t. air) \(n_L = 1.36\) (alcohol w.r.t. air) \(n_{GL} = \frac{1.65}{1.36} \approx 1.21\).

Answer 1

The Correct Option is C

Concept: The refractive index of medium 2 with respect to medium 1 (\(n_{21}\) or \(^1n_2\)) is given by the ratio of the absolute refractive index of medium 2 (\(n_2\)) to the absolute refractive index of medium 1 (\(n_1\)). Absolute refractive index is usually measured with respect to air (or vacuum). \[ n_{21} = \frac{n_2}{n_1} = \frac{\text{Refractive index of medium 2 w.r.t. air}}{\text{Refractive index of medium 1 w.r.t. air}} \] This can also be expressed in terms of speeds of light: \(n_{21} = \frac{v_1}{v_2}\), where \(v_1\) is the speed of light in medium 1 and \(v_2\) is the speed of light in medium 2. Step 1: Identify the given refractive indices (with respect to air) Let \(n_g\) be the refractive index of flint glass with respect to air. Let \(n_a\) be the refractive index of alcohol with respect to air. Given:
\(n_g = 1.65\)
\(n_a = 1.36\) Step 2: Determine what needs to be found We need to find the refractive index of flint glass with respect to alcohol. Let this be \(n_{ga}\) (glass w.r.t. alcohol). Here, flint glass is medium 2 and alcohol is medium 1. So, \(n_{ga} = \frac{n_g}{n_a}\). Step 3: Substitute the given values and calculate \[ n_{ga} = \frac{1.65}{1.36} \] Now, perform the division: \[ 1.65 \div 1.36 \approx 1.2132... \] Rounding to two decimal places, we get \(1.21\). The refractive index of flint glass with respect to alcohol is approximately 1.21. This matches option (3).