Question

In deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of nλ/a. Justify this by suitably dividing the slit to bring out the cancellation.

Answer 1

In deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of nλ/a. Justify this by suitably dividing the slit to bring out the cancellation.

solution : Let width of single slit is a is divided into n smaller slits. if a' is the width of each one of the smaller slits, a' = a/n. ....(1)

now for the single slit to produce zero intensity, each one of the smaller slits should also produce zero intensity.

But this is possible only if,

angle, α = λ/a'

or, α = λ/(a/n) [ from equation (1), ]

or, α = nλ/a

hence, it is clear that, in deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of $\frac{n\lambda}{a}$.

Answer 2

Answer:

Explanation:

In deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of nλ/a. Justify this by suitably dividing the slit to bring out the cancellation.

solution : Let width of single slit is a is divided into n smaller slits. if a' is the width of each one of the smaller slits, a' = a/n. ....(1)

now for the single slit to produce zero intensity, each one of the smaller slits should also produce zero intensity.

But this is possible only if,

angle, α = λ/a'

or, α = λ/(a/n) [ from equation (1), ]

or, α = nλ/a

hence, it is clear that, in deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of .