The monochromatic light diffracts on the two slits which are 0.1 mm apart (their size is negligible) and produces an interference pattern on the wall which is 3 m far from the apparatus. a) The distance between the central bright fringe and the first off-center bright fringe is 2 cm. What is the wavelength of the light? Which color is it? b) How many bright fringes could we see on the wall? c) We change the film with slits and the distance between adjacent dark fringe and bright fringe is 7 mm. What is the distance between two slits now?

a) λ  = 666.7 nm, b) infinity, c)  d = 2,857 10⁻⁴ m = 0.2857 mm

Explanation:

The interference phenomenon is described by Young's equation

          d sin θ = m λ

Where d is the gap separation, λ the wavelength and m the order of interference

Let's use trigonometry for the angle

           tan θ = y / L

As in this we express the angles are very small

          tan θ = sin θ / cos θ = sin θ

We replace

          d y / L = m λ

a) let's look for the wavelength

         λ = d y / L m

The first bright strip occurs for m = 1

Let's calculate

         λ = 0.1 10⁻³  2 10⁻² / 3

         λ = 6.667 10⁻⁷ m

Let's take nm

           λ  = 666.7 nm

this is orange to red

.b) In theory the number of strips is infinite, but in the one made it is determined by the convolution with the diffraction pattern of each slit, which depends on the width of each one.

c) If the new distance y = 7 mm

Which of the separation of the slits

          d = m    λ L / y

          d = 1  666.7 10⁻⁹  3 / 0.007

         d = 2,857 10⁻⁴ m = 0.2857 mm