Let us consider the condition for first minimum with (n = 1). a sin θ = λ
The first minimum has an angular spread of, sin θ = \(\frac{λ}{a}\). Special cases to discuss on the condition.
1. When a < λ, the diffraction is not possible, because sin 0 can never be greater than 1.
2. When a ≥ λ, the diffraction is possible.
- For a = λ, sin θ = 1 i.e, θ = 90°. That means the first minimum is at 90°. Hence, the central maximum spreads fully in to the geometrically shadowed region leading to bending of the diffracted light to 90°.
- For a >> λ, sin θ << 1 i.e, the first minimum will fall within the width of the slit itself. The diffraction will not be noticed at all.
3. When a > λ and also comparable, say a = 2λ, sin θ = \(\frac{λ}{a}\)= \(\frac{λ}{2λ}\) = \(\frac{1}{2}\); then θ = 30°. These are practical cases where diffraction could be observed effectively.
