Light of wavelength 589 nm in vacuum passes through a piece of fused quartz of index of refraction n = 1.458. What is the frequency of the light in fused quartz? [Speed of light c = 3.00×108ms−1

Light of wavelength 589 nm in vacuum passes through a piece of fused quartz of index of refraction n = 1.458. What is the frequency of the light in fused quartz?

[Speed of light c = 3.00×108ms−1
A. 5.09×1015Hz
B. 5.09×1014Hz
C. 1.77× 1015Hz
D. 1.77×1014Hz

Correct Option: Answer is B
The relationship between the speed of light (c), wavelength (λ), and frequency (f) is given by the equation:
c=λ*f
where:
• c is the speed of light in the medium,
• λ is the wavelength,
• f is the frequency.
The refractive index (n) is related to the speed of light in a medium by the equation:
n=v/c
where:
• n is the refractive index,
• c is the speed of light in a vacuum,
• v is the speed of light in the medium.
Since v=nc, the frequency (f) in the medium can be expressed as:
f=λc
Substitute the given values:
f=3.00×108 m/s /589×10−9 m
f≈5.09×1014 Hz
Therefore, the correct answer is:
B. 5.09×1014Hz

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