A slit with a width of 2511 nm has red light of wavelength 650 nm impinge on it. The diffracted light interferes on a surface. At which angle will the first minimum be?

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Step 1 : Check what you are givenWe 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 arelooking to determine the angle to first minimum so we know that

m = 1.

Step 2 : Applicable principlesWe 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 : Substitutionsin θ = (650 × 10−

^{9}m)/(2511 × 10−^{9}m)sin θ = 650/2511

sin θ = 0.258861012

θ = sin−

^{1}0.258861012θ = 15°

The first minimum is at 15 degrees from the centre peak.