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