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 = [tex]3\times 10^{8}\ m/s[/tex]
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
[tex]\frac{d}{\frac{c}{n}} - \frac{d}{v} = 4.8\times 10^{- 9}[/tex]
[tex]\frac{0.8656}{\frac{c}{n}} - \frac{0.865}{v} = 4.8\times 10^{- 9}[/tex]
where
n = refractive index of the medium
v = speed of light in medium
[tex]\frac{0.8656}{\frac{c}{n}} - \frac{0.865}{v} = 4.8\times 10^{- 9}[/tex]
[tex]n = \frac{4.8\times 10^{- 9}\times 3.00\times 10^{8}}{0.865} + 1[/tex]
n = 2.66
Now,
The wavelength in the glass:
[tex]\lambda' = \frac{\lambda }{n}[/tex]
[tex]\lambda' = \frac{570}{2.66} = 213.9\ nm[/tex]
