What is the relationship between the refractive index of a glass plate and the thickness required to permit the same number of wavelengths as a certain length of water column?
The correct thickness of the glass plate that will permit the same number of wavelengths as an 18 cm long column of water is 24 cm.
Understanding Refraction and Wavelengths
Refraction: Refraction is the bending of light as it passes from one medium to another with a different refractive index. This phenomenon causes changes in the speed of light and the direction it travels.
Mechanism of Refraction in Glass and Water
When light passes from air into glass or water, the speed of light changes due to the different refractive indices of the mediums. The refractive index is a measure of how much the speed of light is reduced in a particular medium compared to its speed in a vacuum.
Calculating Thickness for the Same Number of Wavelengths
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 use the formula:
Thickness = (Number of Wavelengths) x (Wavelength) / (Refractive Index)
In this case, the refractive index of the glass plate is 3/2, and the refractive index of water is 4/3. Let's assume the wavelength of light is the same in both cases. Therefore, the thickness of the glass plate will be:
Thickness = (18 cm) x (4/3) / (3/2) = 24 cm
Conclusion
The relationship between the refractive index of a medium and the required thickness to permit the same number of wavelengths is crucial in understanding optics and light behavior. The calculation demonstrated how the different refractive indices of the glass plate and water column affect the necessary thickness for an equal number of wavelengths to pass through each medium.