Answer :
The index of refraction of a medium is the ratio of the speed of light in vacuum to the speed of light in the medium. Here, the refractive index is 1.78.
What is refraction ?
Refraction is the phenomenon in which a light ray bends in its direction when passing from one medium to the other. That is why we see a bend in image of a stick under water compared to the part above water.
The measuring of bending of light by refraction is called refractive index of the medium. It is dependent on the speed of light in each, medium and their densities.
Given the speed of light in a medium = 1.69 × 10⁸ m/s
speed of light in vacuum = 3 × 10⁸ m/s
refractive index = 3 × 10⁸ m/s /1.69 × 10⁸ m/s = 1.78
Therefore, the index of refraction of the material is 1.78.
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Final answer:
The index of refraction of the material where the speed of light is 1.69 × 10^8 m/s is approximately 1.775, calculated using the formula n = c/v.
Explanation:
The index of refraction of a material is defined as the ratio of the speed of light in a vacuum to the speed of light in that material. Using this definition, the index of refraction, n, can be calculated with the formula n = c/v, where c is the speed of light in a vacuum and v is the speed of light in the material.
In this question, we are given the speed of light in a material as 1.69 × 108 m/s. The speed of light in a vacuum is approximately 3.00 × 108 m/s. Thus, the index of refraction n can be calculated as follows:
n = c/v
n = (3.00 × 108 m/s) / (1.69 × 108 m/s)
n ≈ 1.775
Therefore, the index of refraction of the material in question is approximately 1.775.
