The refractive indices of glycerine and diamond with respect to air are 1.4 and 2.4 respectively. Calculate the speed of light in glycerine and diamond. From these results, calculate the refractive index of diamong with respect to glycerine. `(c=3xx10^(8)m//s)`

Options

A. `2.143xx10^(8)m//s, 1.250xx10^(8)m//s, 1.714`
B. `1.143xx10^(8)m//s,1.250xx10^(8)m//s, 1.714`
C. `2.143xx10^(8)m//s,2.250xx10^(8)m//s, 1.714`
D. `2.143xx10^(8)m//s,1.250xx10^(8)m//s,1.514`

Answer

To solve the problem, we need to calculate the speed of light in glycerine and diamond, and then find the refractive index of diamond with respect to glycerine.

### Step 1: Calculate the speed of light in glycerine
The formula to calculate the speed of light in a medium is given by:
\[ V = \frac{C}{n} \]
where:
- \( V \) is the speed of light in the medium,
- \( C \) is the speed of light in vacuum (or air), which is \( 3 \times 10^8 \, \text{m/s} \),
- \( n \) is the refractive index of the medium.

For glycerine, the refractive index \( n_g \) is given as 1.4. Therefore, we can calculate the speed of light in glycerine (\( V_g \)):
\[ V_g = \frac{C}{n_g} = \frac{3 \times 10^8}{1.4} \]

Calculating this gives:
\[ V_g = \frac{3 \times 10^8}{1.4} \approx 2.14 \times 10^8 \, \text{m/s} \]

### Step 2: Calculate the speed of light in diamond
Now, we will calculate the speed of light in diamond. The refractive index \( n_d \) for diamond is given as 2.4. Thus, we can calculate the speed of light in diamond (\( V_d \)):
\[ V_d = \frac{C}{n_d} = \frac{3 \times 10^8}{2.4} \]

Calculating this gives:
\[ V_d = \frac{3 \times 10^8}{2.4} \approx 1.25 \times 10^8 \, \text{m/s} \]

### Step 3: Calculate the refractive index of diamond with respect to glycerine
The refractive index of diamond with respect to glycerine (\( n_{dg} \)) can be calculated using the formula:
\[ n_{dg} = \frac{n_d}{n_g} \]

Substituting the values we have:
\[ n_{dg} = \frac{2.4}{1.4} \]

Calculating this gives:
\[ n_{dg} \approx 1.714 \]

### Summary of Results
- Speed of light in glycerine: \( V_g \approx 2.14 \times 10^8 \, \text{m/s} \)
- Speed of light in diamond: \( V_d \approx 1.25 \times 10^8 \, \text{m/s} \)
- Refractive index of diamond with respect to glycerine: \( n_{dg} \approx 1.714 \)