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kobusy [5.1K]
3 years ago
11

In a physics lab, light with a wavelength of 530 nm travels in air from a laser to a photocell in a time of 16.7 ns . When a sla

b of glass with a thickness of 0.870 m 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 ns to travel from the laser to the photocell.
What is the wavelength of the light in the glass?

Use 3.00×108 m/s for the speed of light in a vacuum. Express your answer using two significant figures.
Physics
1 answer:
Harlamova29_29 [7]3 years ago
5 0

Answer:

\lambda'=78.086\ nm

Explanation:

Given:

  • wavelength of light in the air, \lambda=530\times 10^{-9}\ m
  • time taken to travel from the source to the photocell via air, t=16.7\ s
  • time taken to reach the photocell via air and glass slab, t'=21.3\times 10^{-9}\ s
  • thickness of the glass slab, x=0.87\ m

<u>Now we have the relation for time:</u>

\rm time=\frac{distance}{speed}

hence,

t=\frac{d}{c}

c= speed of light in air

16.7\times 10^{-9}=\frac{d}{3\times 10^8}

d=16.7\times 10^{-9}\times 3\times 10^8

d=5.01\ m

For the case when glass slab is inserted between the path of light:

\frac{(d-x)}{c} +\frac{x}{v} =t' (since light travel with the speed c only in the air)

here:

v = speed of light in the glass

\frac{(5.01-0.87)}{3\times 10^8} +\frac{0.87}{v} =21.3\times 10^{-9}

v=4.42\times 10^7\ m.s^{-1}

Using Snell's law:

\frac{\lambda}{\lambda'} =\frac{c}{v}

\frac{530}{\lambda'} =\frac{3\times 10^8}{4.42\times 10^7}

\lambda'=78.086\ nm

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