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Setler79 [48]
3 years ago
11

In a physics lab, light with a wavelength of 570 travels in air from a laser to a photocell in a time of 16.5 . When a slab of g

lass with a thickness of 0.865 is placed in the light beam, with the beam incident along the normal to the parallel faces of the slab, it takes the light a time of 21.3 to travel from the laser to the photocell. What is the wavelength of the light in the glass? Use 3.00×10^8 m/s for the speed of light in a vacuum.
Physics
1 answer:
aliina [53]3 years ago
5 0

Answer:

Wavelength is calculated as 213.9 nm

Solution:

As per the question:

Wavelength of light = 570 nm

Time, t = 16.5 ns

Thickness of glass slab, d = 0.865 ns

Time taken to travel from laser to the photocell, t' = 21.3

Speed of light in vacuum, c = 3\times 10^{8}\ m/s

Now,

To calculate the wavelength of light inside the glass:

After the insertion of the glass slab into the beam, the extra time taken by light to cover a thickness t = 0.865 m is:

t' - t = 21.3 - 16.5 = 4.8 ns

Thus

\frac{d}{\frac{c}{n}} - \frac{d}{v} = 4.8\times 10^{- 9}

\frac{0.8656}{\frac{c}{n}} - \frac{0.865}{v} = 4.8\times 10^{- 9}

where

n = refractive index of the medium

v = speed of light in medium

\frac{0.8656}{\frac{c}{n}} - \frac{0.865}{v} = 4.8\times 10^{- 9}

n = \frac{4.8\times 10^{- 9}\times 3.00\times 10^{8}}{0.865} + 1

n = 2.66

Now,

The wavelength in the glass:

\lambda' = \frac{\lambda }{n}

\lambda' = \frac{570}{2.66} = 213.9\ nm

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