Question

Two slits are spaced 0.33mm apart. If the angle between the first dark fringe and the central maximum is 0.055º, what is the wavelength of a light falling on these two slits?

Answer 1

`6.33\cdot 10^(-7) m`

Step-by-step explanation:

The condition for the first minimum (= first dark fringe) in the interference pattern produced by diffraction from a double slit is

`d sin \theta = (\lambda)/(2)`

where

`d=0.33 mm = 0.33\cdot 10^(-3)m` is the separation between the slits

`\theta=0.055^(\circ)` is the angle of the first minimum

`\lambda` is the wavelength

Solving the equation for the wavelength, we find

`\lambda = 2 d sin \theta = 2(0.33\cdot 10^(-3) m)sin 0.055^(\circ)=6.33\cdot 10^(-7) m`