A light ray travels from air into a glass medium with a refractive index of 1.5. If the speed of light in air

Question

A light ray travels from air into a glass medium with a refractive index of 1.5. If the speed of light in air is 3 x 10^8 m/s, what is the speed of light in the glass?

Examoogle · Accepted Answer

The correct answer is Option A: 2 	imes 10^8 	ext{ m/s}. The speed of light in a medium is determined by the refractive index of that medium. Using the formula $v = rac{c}{n}$, where $c$ is the speed of light in vacuum (or air) and $n$ is the refractive index, we find that the speed of light in glass is $2 imes 10^8 ext{ m/s}$.

Step-by-Step Solution & Concepts:
The speed of light in a medium is determined by the refractive index of that medium. Using the formula $v = rac{c}{n}$, where $c$ is the speed of light in vacuum (or air) and $n$ is the refractive index, we find that the speed of light in glass is $2 imes 10^8 ext{ m/s}$.

Working Principle: Refractive index ($n$) is defined as the ratio of the speed of light in a vacuum or air ($c$) to the speed of light in the medium ($v$). When light enters a denser optical medium like glass ($n = 1.5$), it slows down proportionally to that refractive index.

Key Formulas: $n = rac{c}{v}$ — Refractive index formula; $v = rac{c}{n}$ — Speed of light in a medium

Key Points: The refractive index is a dimensionless quantity greater than or equal to 1.; Light travels fastest in a vacuum and slows down in material media.; The frequency of light remains unchanged when it enters a new medium, but its wavelength and speed decrease.

Applications: Design of optical lenses and fiber optics; Understanding total internal reflection in diamonds and optical fibers

Additional Info: Speed of light in vacuum $c \approx 3 imes 10^8 ext{ m/s}$.. Calculation: $v = rac{3 imes 10^8}{1.5} = 2 imes 10^8 ext{ m/s}$. Option A is correct.

Answer: A is correct — The speed of light in glass with a refractive index of 1.5 is calculated as $3 imes 10^8 / 1.5 = 2 imes 10^8 ext{ m/s}$.

Exam Tip: Always ensure units are consistent when dealing with speed and refractive index problems in physics exams.

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Option B: 5 	imes 10^8 	ext{ m/s}

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Option C: 5 	imes 10^8 	ext{ m/s}

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Option D: 3 	imes 10^8 	ext{ m/s}

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