Answer :
Answer:
To find the refractive index of water with respect to diamond (\( n_{\text{water/diamond}} \)) and diamond with respect to water (\( n_{\text{diamond/water}} \)), we use the formula for refractive index:
\[ n = \frac{c}{v} \]
where:
- \( c \) is the speed of light in vacuum (\( 3.00 \times 10^8 \) m/s),
- \( v \) is the speed of light in the medium.
Given:
- Speed of light in water (\( v_{\text{water}} \)) = \( 2.25 \times 10^8 \) m/s
- Speed of light in diamond (\( v_{\text{diamond}} \)) = \( 1.25 \times 10^8 \) m/s
### i. Refractive index of water with respect to diamond (\( n_{\text{water/diamond}} \)):
\[ n_{\text{water/diamond}} = \frac{c}{v_{\text{water}}} = \frac{3.00 \times 10^8 \, \text{m/s}}{2.25 \times 10^8 \, \text{m/s}} \]
\[ n_{\text{water/diamond}} = \frac{3.00}{2.25} \]
\[ n_{\text{water/diamond}} = 1.33 \]
So, the refractive index of water with respect to diamond is \( \boxed{1.33} \).
### ii. Refractive index of diamond with respect to water (\( n_{\text{diamond/water}} \)):
\[ n_{\text{diamond/water}} = \frac{c}{v_{\text{diamond}}} = \frac{3.00 \times 10^8 \, \text{m/s}}{1.25 \times 10^8 \, \text{m/s}} \]
\[ n_{\text{diamond/water}} = \frac{3.00}{1.25} \]
\[ n_{\text{diamond/water}} = 2.40 \]
So, the refractive index of diamond with respect to water is \( \boxed{2.40} \).
These are the refractive indices for water with respect to diamond and diamond with respect to water, respectively.