Question

Coherent light of wavelength 540 nm passes through a pair of thin slits that are 3.4 × 10-5 m apart. At what angle away from the centerline does the second bright fringe occur?

Answer 1

Answer:
`1.8\°`

Step-by-step explanation:

The diffraction angles
`\theta_(n)` when we have a slit divided into
`n` parts are obtained by the following equation:

`dsin\theta_(n)=n\lambda` (1)

Where:

`d=3.4(10)^(-5)m` is the width of the slit

`\lambda=540 nm=540(10)^(-9)m` is the wavelength of the light

`n` is an integer different from zero.

Now, the second-order diffraction angle is given when
`n=2`, hence equation (1) becomes:

`dsin\theta_(2)=2\lambda` (2)

Now we have to find the value of
`\theta_(2)`:

`sin\theta_(2)=(2\lambda)/(d)` (3)

Then:

`\theta_(2)=arcsin((2\lambda)/(d))` (4)

`\theta_(2)=arcsin((2(540(10)^(-9)m))/(3.4(10)^(-5)m))` (5)

Finally:

`\theta_(2)=1.8\°` (6)