Wavelength Calculation Dilemma: A Case of Potential Error

What is the wavelength of a helium-neon laser beam in an unknown liquid if it takes 1.38 ns to travel through 30.0 cm of the liquid? A) 656 nm B) 645 nm C) 620 nm D) 611 nm

Final answer: By calculating the refractive index of the unknown liquid and using it to find the new wavelength of light in the liquid, we find the wavelength to be approximately 422 nm. However, this answer is not found among the options given, suggesting a potential mistake in the question or data.

Explanation:

The question is about determining the wavelength of a helium-neon laser beam in an unknown liquid. To solve this, we use the concept of refractive index, which is calculated by dividing the speed of light in vacuum by the speed of light in a medium. The speed of light in the unknown liquid is determined by dividing the distance traveled (30.0 cm) by the time taken (1.38 ns). So, the refractive index (n) is approximately 1.498. As per the formula, λ = λ₀ / n, where λ₀ is the wavelength of the laser beam in air (633 nm), the wavelength of the laser beam in the liquid is therefore 422 nm. But since none of the given options match this value, there might be a mistake in the original question or data provided.

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