Final answer:
The correct thickness of the glass plate that will permit the same number of wavelengths as an 18 cm long column of water is 16 cm.
Step-by-step explanation:
The refractive index of a material determines how much it can bend light waves. In this case, the refractive index of the glass plate is given as 3/2, while the refractive index of water is 4/3. To find the correct thickness of the glass plate that will permit the same number of wavelengths as an 18 cm long column of water, we need to consider the ratio of their refractive indices. The ratio of the thicknesses is equal to the inverse ratio of the refractive indices:
Thickness of glass plate / Thickness of water = refractive index of water / refractive index of glass plate
Substituting the given values:
Thickness of glass plate / 18 cm = (4/3) / (3/2)
Thickness of glass plate = (4/3) / (3/2) * 18 cm
Simplifying the expression, we get:
Thickness of glass plate = 16 cm
Therefore, the correct thickness of the glass plate that will permit the same number of wavelengths as an 18 cm long column of water is 16 cm (Option B).