Answer :
To solve this problem, we need to determine the refractive index of glass with respect to water, given the refractive indices of water with respect to air and glass with respect to air.
### Step-by-Step Solution:
1. Identify Given Values:
- Refractive index of water with respect to air ([tex]\( n_{water/air} \)[/tex]): 1.33
- Refractive index of glass with respect to air ([tex]\( n_{glass/air} \)[/tex]): 1.5
2. Understand the Concept:
- The refractive index of one medium with respect to another is a comparative measure of how much the speed of light is reduced in those two media.
3. Using the Refractive Index Relationship:
- The refractive index of glass with respect to water ([tex]\( n_{glass/water} \)[/tex]) can be found using the relationship:
[tex]\[ n_{glass/water} = \frac{n_{glass/air}}{n_{water/air}} \][/tex]
where [tex]\( n_{glass/air} \)[/tex] is the refractive index of glass with respect to air, and [tex]\( n_{water/air} \)[/tex] is the refractive index of water with respect to air.
4. Perform the Calculation:
- Substitute the given values into the relationship:
[tex]\[ n_{glass/water} = \frac{1.5}{1.33} \][/tex]
5. Compute the Result:
- Division of 1.5 by 1.33 results in approximately:
[tex]\[ n_{glass/water} \approx 1.1278 \][/tex]
Therefore, the refractive index of glass with respect to water is approximately 1.1278.
### Step-by-Step Solution:
1. Identify Given Values:
- Refractive index of water with respect to air ([tex]\( n_{water/air} \)[/tex]): 1.33
- Refractive index of glass with respect to air ([tex]\( n_{glass/air} \)[/tex]): 1.5
2. Understand the Concept:
- The refractive index of one medium with respect to another is a comparative measure of how much the speed of light is reduced in those two media.
3. Using the Refractive Index Relationship:
- The refractive index of glass with respect to water ([tex]\( n_{glass/water} \)[/tex]) can be found using the relationship:
[tex]\[ n_{glass/water} = \frac{n_{glass/air}}{n_{water/air}} \][/tex]
where [tex]\( n_{glass/air} \)[/tex] is the refractive index of glass with respect to air, and [tex]\( n_{water/air} \)[/tex] is the refractive index of water with respect to air.
4. Perform the Calculation:
- Substitute the given values into the relationship:
[tex]\[ n_{glass/water} = \frac{1.5}{1.33} \][/tex]
5. Compute the Result:
- Division of 1.5 by 1.33 results in approximately:
[tex]\[ n_{glass/water} \approx 1.1278 \][/tex]
Therefore, the refractive index of glass with respect to water is approximately 1.1278.
