A monochromatic beam of light in air has a wavelength of 454 nm in air.It passes through glass (n = 1.52)and then through carbon disulfide (n = 1.63).What is its wavelength in the carbon disulfide?
A) 279 nm
B) 740 nm
C) 423 nm
D) 487 nm
E) 299 nm

Question

A monochromatic beam of light in air has a wavelength of 454 nm in air.It passes through glass (n = 1.52)and then through carbon disulfide (n = 1.63).What is its wavelength in the carbon disulfide?
A) 279 nm
B) 740 nm
C) 423 nm
D) 487 nm
E) ​299 nm

Quizplus · Accepted Answer

The wavelength of light in a medium is given by the equation:$$\lambda = \frac{c}{n
u}$$where:* $$\lambda$$ is the wavelength in meters* c is the speed of light in a vacuum* n is the index of refraction of the medium* $$
u$$ is the frequency of the lightIn this problem, the wavelength of the light in air is 454 nm. The index of refraction of glass is 1.52, and the index of refraction of carbon disulfide is 1.63. We want to find the wavelength of the light in carbon disulfide.We can use the equation above to solve for the wavelength in carbon disulfide:$$\lambda_{cs} = \frac{c}{n_{cs}
u}$$We know that the frequency of the light does not change when it passes from one medium to another. Therefore, we can substitute the frequency of the light in air into the equation above:$$\lambda_{cs} = \frac{c}{n_{cs}
u_{air}}$$We can now substitute the values we know into the equation:$$\lambda_{cs} = \frac{3	imes10^8 m/s}{1.63	imes4.67	imes10^{14} Hz}$$$$\lambda_{cs} = 279 nm$$Therefore, the wavelength of the light in carbon disulfide is 279 nm.

A Monochromatic Beam of Light in Air Has a Wavelength