The refractive index of water is \(\frac{4}{3}\) and for glass it is \(\frac{3}{2},\) w.r.t. water it is _____
Understanding Refractive Index Calculation
The refractive index of a medium tells us how much light bends when it enters that medium from a vacuum or air. It is defined as the ratio of the speed of light in vacuum (\(c\)) to the speed of light in the medium (\(v\)).
\(n = \frac{c}{v}\)
When we talk about the refractive index of one medium with respect to another, it's called the relative refractive index. The relative refractive index of medium 2 with respect to medium 1 (\(n_{12}\) or \(_1n_2\)) is given by the ratio of the absolute refractive index of medium 2 (\(n_2\)) to the absolute refractive index of medium 1 (\(n_1\)).
\(n_{12} = \frac{n_2}{n_1}\)
Calculating Refractive Index of Glass with Respect to Water
We are given the following information:
- Refractive index of water (\(n_w\)) = \(\frac{4}{3}\) (This is usually with respect to vacuum or air, i.e., absolute refractive index of water).
- Refractive index of glass (\(n_g\)) = \(\frac{3}{2}\) (This is also usually with respect to vacuum or air, i.e., absolute refractive index of glass).
We need to find the refractive index of glass with respect to water. Using the formula for relative refractive index, we have:
\(n_{gw} = \frac{\text{Absolute refractive index of glass}}{\text{Absolute refractive index of water}} = \frac{n_g}{n_w}\)
Step-by-Step Calculation
Substitute the given values into the formula:
\(n_{gw} = \frac{\frac{3}{2}}{\frac{4}{3}}\)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
\(n_{gw} = \frac{3}{2} \times \frac{3}{4}\)
Now, multiply the numerators together and the denominators together:
\(n_{gw} = \frac{3 \times 3}{2 \times 4} = \frac{9}{8}\)
Therefore, the refractive index of glass with respect to water is \(\frac{9}{8}\).
Summary of Calculation
| Quantity | Value |
|---|---|
| Absolute refractive index of water (\(n_w\)) | \(\frac{4}{3}\) |
| Absolute refractive index of glass (\(n_g\)) | \(\frac{3}{2}\) |
| Refractive index of glass w.r.t. water (\(n_{gw}\)) | \(\frac{n_g}{n_w} = \frac{3/2}{4/3} = \frac{3}{2} \times \frac{3}{4} = \frac{9}{8}\) |
The calculated value matches one of the given options.
Revision Table: Key Refractive Index Concepts
| Concept | Definition/Formula | Notes |
|---|---|---|
| Absolute Refractive Index (\(n\)) | \(n = \frac{c}{v}\) | Speed of light in vacuum (\(c\)) vs. in medium (\(v\)). \(n\) is always \(\ge 1\). |
| Relative Refractive Index (\(n_{12}\) or \(_1n_2\)) | \(_1n_2 = \frac{n_2}{n_1}\) | Refractive index of medium 2 with respect to medium 1. Relates absolute indices. |
| Relation with Wavelength (\(\lambda\)) | \(n \propto \frac{1}{\lambda}\) | Refractive index is inversely proportional to the wavelength of light in the medium. |
| Relation with Speed of Light (\(v\)) | \(n \propto \frac{1}{v}\) | Refractive index is inversely proportional to the speed of light in the medium. |
Additional Information on Refractive Index and Light Propagation
The concept of refractive index is fundamental to understanding how light behaves as it passes from one medium to another. When light crosses the boundary between two media with different refractive indices, it changes speed and direction. This phenomenon is known as refraction.
- Denser vs. Rarer Medium: A medium with a higher refractive index is optically denser than a medium with a lower refractive index. Light bends towards the normal when moving from a rarer to a denser medium, and away from the normal when moving from a denser to a rarer medium.
- Snell's Law: The relationship between the angles of incidence and refraction and the refractive indices of the two media is described by Snell's Law: \(n_1 \sin \theta_1 = n_2 \sin \theta_2\), where \(n_1\) and \(n_2\) are the refractive indices of the two media, and \(\theta_1\) and \(\theta_2\) are the angles of incidence and refraction, respectively.
- Dependence on Wavelength: The refractive index of a medium also depends slightly on the wavelength (or color) of light. This is called dispersion and is the reason prisms can split white light into its constituent colors. Generally, refractive index is higher for shorter wavelengths (like blue light) and lower for longer wavelengths (like red light).
Understanding relative refractive index is crucial for solving problems involving light passing through multiple layers of different materials, such as in lenses, prisms, and optical fibers.
Important Questions from Polarization by Reflection
What is the absolute refractive index of kerosene?
The refractive index of water \(_a\mu_w=\frac{4}{3}\) and refractive index of glass \(_a\mu_g=\frac{3}{2}\) . A lens placed in air has focal length 10 cm. What will be its focal length if placed inside water?
The refractive index of water and dense flint glass are 1.33 and 1.65, respectively. A ray of light travels from dense flint glass to water. The refractive index of water with respect to dense flint glass is _______ and the light ray bends _______ the normal in water.
The refractive indices of quartz crystal for right handed and left handed circularly polarized light of wavelength 762.9 nm are 1.5391 and 1.5392 respectively. The angle of rotation produced by the crystal plate of thickness 0.5 mm is:
A ray of light is incident on a transparent medium at an angle of 60°. The reflected ray of light is found to be completely polarised. Then, the refractive index of the transparent medium is nearly:
