The speed of light in amber is $1.94 * 10^{8} m / s$. What is the index of refraction for amber?
Answer (1)
Define the index of refraction as the ratio of the speed of light in vacuum to the speed of light in the medium.
Use the formula n = v c , where c = 3.00 × 1 0 8 m / s and v = 1.94 × 1 0 8 m / s .
Substitute the values into the formula: n = 1.94 × 1 0 8 3.00 × 1 0 8 = 1.94 3.00 .
Calculate the index of refraction: n ≈ 1.54639 .
Explanation
Understanding the Problem We are given that the speed of light in amber is 1.941 0 8 m / s . We need to find the index of refraction for amber. The index of refraction is defined as the ratio of the speed of light in vacuum to the speed of light in the medium.
Defining Variables The speed of light in vacuum is approximately 3.001 0 8 m / s . Let v be the speed of light in amber, which is 1.941 0 8 m / s . Let c be the speed of light in vacuum, which is approximately 3.001 0 8 m / s . Let n be the index of refraction of amber.
Stating the Formula The formula for the index of refraction is given by: n = v c where n is the index of refraction, c is the speed of light in vacuum, and v is the speed of light in the medium.
Calculating the Index of Refraction Substitute the given values into the formula: n = 1.94 × 1 0 8 3.00 × 1 0 8 n = 1.94 3.00 n ≈ 1.54639
Final Answer Since the problem asks for the answer with no unit, we provide the calculated value of n .
Examples
Understanding the index of refraction is crucial in optics, particularly when designing lenses for eyeglasses or cameras. For instance, if an optometrist knows the index of refraction of the lens material, they can accurately calculate the curvature needed to focus light correctly onto the retina, ensuring clear vision. Similarly, in photography, knowing the index of refraction of lens elements helps in minimizing aberrations and maximizing image sharpness. This concept also extends to fiber optics, where the index of refraction difference between the core and cladding materials determines how light is guided through the fiber, enabling high-speed data transmission.
