Question

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 slab 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.

Answer 1

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, $x=0.87\ m$

Now we have the relation for time:

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

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:

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

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

$\lambda'=78.086\ nm$