Refractive index of glass with respect to water is 5/4 and the refractive index of water with respect to air is 4/3, what is the refractive index of glass with respect to air?

A. 5/3

B. 5/4

C. 16/15

D. 1.5

To find the refractive index of glass with respect to air, we can use the relationship between the refractive indices of the materials involved. The refractive index of a medium is defined as the ratio of the speed of light in a vacuum to the speed of light in that medium. When dealing with multiple media, we can relate their refractive indices using the following formula:

Understanding the Relationships

We have two refractive indices given:

• The refractive index of glass with respect to water, denoted as n_gw = 5/4.
• The refractive index of water with respect to air, denoted as n_wa = 4/3.

We want to find the refractive index of glass with respect to air, denoted as n_ga. We can use the relationship:

Formula Derivation

The refractive index of glass with respect to air can be calculated using the following formula:

n_ga = n_gw × n_wa

Substituting the values we have:

n_ga = (5/4) × (4/3)

Calculating the Result

Now, let's perform the multiplication:

n_ga = (5 × 4) / (4 × 3) = 20 / 12

This fraction can be simplified:

20 / 12 = 5 / 3

Final Answer

Thus, the refractive index of glass with respect to air is 5/3. Therefore, the correct option is:

A. 5/3

This calculation shows how refractive indices can be interconnected through their relationships, allowing us to derive new values based on known ones. Understanding these relationships is crucial in optics and helps in various applications, such as lens design and understanding light behavior in different media.