Question

In a physics lab, light with a wavelength of 490 nm travels in air from a laser to a photocell in a time of 16.6 ns. When a slab of glass with a thickness of 0.800 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 21.0 ns to travel from the laser to the photocell. Use 3.00x108 m/s for the speed of light in a vacuum. Express your answer using two significant figures. O ? % AC 1 = 280 Submit Previous

Answer 1

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

$d=v\times t$

$d=3\times10^{8}\times16.6\times10^{-9}$

$d=4.98\ m$

After slab,

We need to calculate the time to cross air

Using formula of time

$t=\dfrac{d}{v}$

Put the value into the formula

$t=\dfrac{4.98-0.800}{3\times10^{8}}$

$t=13.9\times10^{-9}\ s$

$t=13.9\ ns$

So the time in slab is

$t'=21.0-t$

Put the value into the formula

$t'=21.0\ ns-13.9\ ns$

$t'=7.1\ ns$

We need to calculate the speed in slab

Using formula of speed

$v=\dfrac{0.8}{t'}$

Put the value into the formula

$v=\dfrac{0.8}{7.1\times10^{-9}}$

$v=1.12\times10^{8}\ m/s$

We need to calculate the wavelength

Using relation of wavelength and speed

$\dfrac{c_{1}}{c_{2}}=\dfrac{\lambda_{1}}{\lambda_{2}}$

Put the value into the formula

$\dfrac{3\times10^{8}}{1.12\times10^{8}}=\dfrac{490\times10^{-9}}{\lambda_{2}}$

$\lambda_{2}=\dfrac{490\times10^{-9}\times1.12\times10^{8}}{3\times10^{8}}$

$\lambda_{2}=182.9\ nm$

Hence, The wavelength of the light in the glass is 182.9 nm.