The absolute refractive index of benzene is 1.5 and the refractive index of kerosene is 1.44

The absolute refractive index of benzene is 1.5 and the refractive index of kerosene is 1.44. Find the relative refractive index of benzene with respect to kerosene.

The correct answer and explanation is:

Answer:
The relative refractive index of benzene with respect to kerosene is approximately 1.042.

Explanation:

The absolute refractive index (also called the refractive index) of a medium is defined as the ratio of the speed of light in vacuum to the speed of light in that medium: n=cvn = \frac{c}{v}

where:

• nn = absolute refractive index of the medium
• cc = speed of light in vacuum (about 3×1083 \times 10^8 m/s)
• vv = speed of light in the medium

When we talk about relative refractive index of one medium with respect to another, it means how much the speed of light changes when it goes from the second medium into the first medium. It can be calculated by dividing the absolute refractive index of the first medium by the absolute refractive index of the second medium: nrelative=n1n2n_{\text{relative}} = \frac{n_1}{n_2}

Here:

• n1n_1 = absolute refractive index of benzene = 1.5
• n2n_2 = absolute refractive index of kerosene = 1.44

So, nrelative=1.51.44≈1.0417≈1.042n_{\text{relative}} = \frac{1.5}{1.44} \approx 1.0417 \approx 1.042

What does this mean physically?

The relative refractive index of benzene with respect to kerosene tells us how much the speed of light slows down when it passes from kerosene into benzene. A relative refractive index greater than 1 means light travels slower in benzene compared to kerosene.

Since benzene has a higher absolute refractive index, light slows down more in benzene than in kerosene. This difference affects how light bends or refracts at the interface between these two liquids, which is important in optics and applications such as microscopy, lens design, and chemical analysis.

Additional context:

• The refractive index is a dimensionless number and depends on the wavelength of light and the properties of the medium (like density and molecular structure).
• When light passes from one medium to another, Snell’s law uses the relative refractive index to determine the angle of refraction: nrelative=sin⁡θ2sin⁡θ1n_{\text{relative}} = \frac{\sin \theta_2}{\sin \theta_1}
• The closer the refractive indices of two media are, the less light bends at their interface.

This relative refractive index is fundamental in understanding how light behaves between two materials and is widely used in optics and materials science.