Interesting Physics Question About Refractive Index
Have you ever wondered how the refractive index of different materials affects the thickness required to permit the same number of wavelengths of light? Let's solve a physics problem together!
The refractive index of a material is defined as the ratio of the speed of light in vacuum to the speed of light in that material. In this case, we need to find the correct thickness of a glass plate that will allow the same number of wavelengths of light as an 18 cm long column of water. Let's assume the wavelength of light in water is λwater and the thickness of the glass plate is t. From the given information, the refractive index of the glass plate, nglass, is 32. The refractive index of water, nwater, is 1.333 (given in the reference). Using the formula for refractive index, n = c/v, where c is the speed of light in vacuum and v is the speed of light in the medium, we can write: nglass = c / vglass nwater = c / vwater Since the speed of light in vacuum is the same for both the glass plate and water, we can equate the two equations: nglass = nwater c / vglass = c / vwater Simplifying the equation, we get: vglass = vwater The speed of light in a medium is related to its refractive index and the speed of light in vacuum by the equation: v = c / n Substituting the values, we get: vglass = c / nglass vwater = c / nwater Equating the two equations, we have: c / nglass = c / nwater Simplifying again, we get: nglass = nwater From this equation, we can find the ratio of the thicknesses of the glass plate and water: t / 18 cm = nglass / nwater Substituting the values, we get: t / 18 cm = 32 / 1.333 Simplifying, we find: t / 18 cm = 24 Therefore, the correct thickness of the glass plate is 24 cm. But since the options provided are in centimeters, the correct option is 4 cm (C).
Understanding Refractive Index and Wavelengths
Refractive Index: Refractive index is a measure of how much a ray of light bends when it passes from one medium to another. A higher refractive index indicates a greater bending of light.
Calculating Thickness Based on Refractive Index
When comparing the refractive indices of two different materials, we can determine the thickness of a material required to allow the same number of wavelengths of light to pass through. This calculation involves understanding the speed of light in different media and how it relates to the refractive index.
Significance of Correct Thickness
Ensuring the correct thickness of a material based on refractive index is crucial for various applications such as lens design, optical instruments, and telecommunications. Incorrect thickness can lead to distortion or loss of clarity in transmitted light.