Respuesta :
Answer:
The wavelength of the light in the glass is 182.9 nm.
Explanation:
Given that,
Wavelength = 490 nm
Time = 16.6 ns
Thickness = 0.800 m
Suppose, we need to find the wavelength of the light in the glass.
We need to calculate the distance
Using formula of distance
[tex]d=v\times t[/tex]
[tex]d=3\times10^{8}\times16.6\times10^{-9}[/tex]
[tex]d=4.98\ m[/tex]
After slab,
We need to calculate the time to cross air
Using formula of time
[tex]t=\dfrac{d}{v}[/tex]
Put the value into the formula
[tex]t=\dfrac{4.98-0.800}{3\times10^{8}}[/tex]
[tex]t=13.9\times10^{-9}\ s[/tex]
[tex]t=13.9\ ns[/tex]
So the time in slab is
[tex]t'=21.0-t[/tex]
Put the value into the formula
[tex]t'=21.0\ ns-13.9\ ns[/tex]
[tex]t'=7.1\ ns[/tex]
We need to calculate the speed in slab
Using formula of speed
[tex]v=\dfrac{0.8}{t'}[/tex]
Put the value into the formula
[tex]v=\dfrac{0.8}{7.1\times10^{-9}}[/tex]
[tex]v=1.12\times10^{8}\ m/s[/tex]
We need to calculate the wavelength
Using relation of wavelength and speed
[tex]\dfrac{c_{1}}{c_{2}}=\dfrac{\lambda_{1}}{\lambda_{2}}[/tex]
Put the value into the formula
[tex]\dfrac{3\times10^{8}}{1.12\times10^{8}}=\dfrac{490\times10^{-9}}{\lambda_{2}}[/tex]
[tex]\lambda_{2}=\dfrac{490\times10^{-9}\times1.12\times10^{8}}{3\times10^{8}}[/tex]
[tex]\lambda_{2}=182.9\ nm[/tex]
Hence, The wavelength of the light in the glass is 182.9 nm.
