Question

A beam of yellow light is made to pass through two slits that are 3.0 x 10−3 meters apart. On a screen 2.0 meters away from the slits, an interference pattern appears with bands of light separated by 3.9 x 10−4 meters. What is the wavelength of the light?

3.6 x 10−8 m
5.9 x 10−7 m
6.5 x 10−7 m
3.9 x 10−6 m

Answer 1

The wavelength of the light is
`5.9*10^(-7)m`.

Step-by-step explanation:

The band separation
`\Delta y` for a light wave of wavelength
`\lambda` is given by

`\Delta y = (\lambda L)/(d),`

where
`d` is the slit separation, and
`L` is the distance to the screen.

Solving the above equation of wavelength
`\lambda` we get:

`\lambda = (\Delta y \:d)/(L).`

Now, in our case

`\Delta y = 3.9*10^(-4)m`

`d= 3.0*10^(-3)m`,

and
`L = 2.0m`;

therefore,

`\lambda = (3.9*10^(-4)m *3.0*0^(-3)m)/(2.0m).`

`\boxed{\lambda = 5.9*10^(-7)m,}`

which is the 2nd choice from the options given.