Question

Light shines through a single 8.60 x 10^–4 m slit. A diffraction pattern forms on a screen 5.00 m away. The separation between the middle of the central maximum and the first dark fringe is 4.5 mm. Calculate the wavelength of the light.

Answer 1

Given:

The separation between the slits is,

`d=8.60*10^(-4)\text{ m}`

The distance between the slit and the screen is,

`D=5.00\text{ m}`

The separation between the central maximum and the first dark fringe is,

`\begin{gathered} y=4.5\text{ mm} \\ =4.5*10^(-3)\text{ m} \end{gathered}`

To find:

The wavelength of the light

Step-by-step explanation:

The diagram of the arrangement is shown below:

The separation between the central fringe and the mth bright fringe is,

`dsin\theta=m\lambda`

Here,

`\begin{gathered} m=1 \\ tan\theta=(y)/(D) \\ tan\theta=(4.5*10^(-3))/(5.00) \\ \theta=tan^(-1)(9*10^(-4)) \\ \theta=0.051\degree \end{gathered}`

Now we can write,

`\begin{gathered} 8.60*10^(-4)* sin(0.051\degree)=1*\lambda \\ \lambda=7.65*10^(-7)\text{ m} \end{gathered}`

Hence, the wavelength is

`7.65*10^(-7)\text{ m}`