Equivalent Thickness of Glass Plate Compared to Water Column
What is the relationship between the refractive index of glass plate and water in determining their equivalent thickness?
The refractive index of glass plate is 3/2 and the refractive index of water is 4/3. To determine the equivalent thickness of a glass plate compared to an 18 cm long column of water, we need to consider their refractive indices.
Calculating Equivalent Thickness
Optical Path Length (OPL) Formula: OPL = n * t, where n is the refractive index and t is the physical thickness.
To find the equivalent thickness of the glass plate that will permit the same number of wavelengths as the 18 cm long water column, we set the OPLs of glass and water equal to each other and solve for the unknown thickness of the glass plate.
Given:
Refractive index of glass (nGlass) = 3/2
Refractive index of water (nWater) = 4/3
Physical thickness of water (tWater) = 18 cm
Equation:
nWater * tWater = nGlass * tGlass
Substitute the values:
(4/3) * 18 = (3/2) * tGlass
Solve for tGlass:
tGlass = (4/3 * 18) / (3/2)
tGlass = 24 cm
Therefore, the correct thickness of the glass plate that will permit the same number of wavelengths as the 18 cm long water column is 24 cm.