In a diffraction slit, light at a frequence f has its second null directed at 45◦ from the horizontal direction of the beam. Will there be a distinct third null present in the diffraction pattern?

NO

Explanation:

The angular position of a diffraction null is given by

Asinθ=m λ=m c/f

Given that A is the slit width,

and m is an integer.

The wavelength of the second null satisfies

λ = A sinθ₁/2

of which if there were distinct third null it will satisfy

sinθ₂=3λ/A = 3 * sin 45/2

λ = (3*0.7071) / 2

λ=2.121/2

λ=1.060

Of which 1.060 is greater than 1