Refractive Index of air = 1.003. Thickness of air column has one more wavelength of yellow light.Then the same thickness of vacuum is ?

To determine the thickness of a vacuum column that corresponds to the same optical path length as an air column with a refractive index of 1.003 and an additional wavelength of yellow light, we need to understand how the refractive index affects the propagation of light through different media.

Understanding Refractive Index

The refractive index (n) of a medium is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in that medium (v). For air, the refractive index is slightly greater than 1, indicating that light travels a bit slower in air than in a vacuum. The formula is:

n = c / v

Calculating Optical Path Length

The optical path length (OPL) is given by the product of the refractive index and the physical length of the medium through which light travels. In this case, for the air column, the OPL can be expressed as:

OPL (air) = n (air) × thickness (air)

Given that the refractive index of air is 1.003 and the thickness of the air column corresponds to one wavelength of yellow light, we can denote the wavelength of yellow light as λ. Therefore, the OPL for the air column becomes:

OPL (air) = 1.003 × thickness (air)

Relating Air and Vacuum

In a vacuum, the refractive index is 1, which means that the optical path length is simply the physical length. Thus, for a vacuum column of the same thickness, the OPL can be expressed as:

OPL (vacuum) = thickness (vacuum)

Setting the Equations Equal

Since we want the optical path lengths to be equal, we can set the two equations equal to each other:

1.003 × thickness (air) = thickness (vacuum)

Finding the Thickness of the Vacuum Column

To find the thickness of the vacuum column, we can rearrange the equation:

thickness (vacuum) = 1.003 × thickness (air)

This means that the thickness of the vacuum column must be 1.003 times the thickness of the air column to achieve the same optical path length.

Conclusion

In summary, if the thickness of the air column is equal to one wavelength of yellow light, the corresponding thickness of the vacuum column would be approximately 1.003 times that wavelength. This relationship highlights how the refractive index influences the behavior of light in different media, allowing us to make precise calculations about light propagation.