If the absolute refractive indices of water and glass are 4/3 and 3/2…

The refractive index of one medium with respect to another compares how much each medium bends light relative to a common reference. The refractive index of medium B with respect to medium A is defined as the ratio of B's absolute refractive index to A's absolute refractive index: (refractive index of B with respect to A) = (absolute refractive index of B) divided by (absolute refractive index of A).

1. Absolute refractive index of water, n(water) = 4/3, and absolute refractive index of glass, n(glass) = 3/2, are given directly in the question.

2. The refractive index of glass with respect to water is the ratio n(glass) divided by n(water).

3. Substituting the values: (3/2) divided by (4/3).

4. Dividing by a fraction means multiplying by its reciprocal: (3/2) multiplied by (3/4) equals 9/8.

As an independent check, compute the reverse-order ratio and confirm the two are mutually consistent:

1. The reverse-order ratio, water's absolute refractive index divided by glass's, is n(water) divided by n(glass) = (4/3) divided by (3/2) = (4/3) multiplied by (2/3) = 8/9.

2. Multiplying the two computed ratios together gives (9/8) multiplied by (8/9) = 1, confirming the two values are mutually consistent reciprocals, so 9/8 is correct.

So the refractive index of glass with respect to water is 9/8.