Step 1 : Check what you are given
We know that we are dealing with interference patterns from the
diffraction of light passing through a slit. The slit has a width of
2511 nm which is 2511 × 10−⁹ m and we know that the wavelength of the light is 650 nm which is 650 × 10−⁹ m. We are
looking to determine the angle to first minimum so we know that
m = 1.

Step 2 : Applicable principles
We know that there is a relationship between the slit width, wavelength and interference minimum angles:
sin θ = mλ
a
We can use this relationship to find the angle to the minimum by
substituting what we know and solving for the angle.
Step 3 : Substitution
sin θ = (650 × 10−⁹m)/(2511 × 10−⁹m)
sin θ = 650/2511
sin θ = 0.258861012
θ = sin−¹ 0.258861012
θ = 15°
The first minimum is at 15 degrees from the centre peak.