Question

In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band?

Answer 1

we know the relation between width of slit(d), wavelength$\lambda$ and angular width of central Maxima $\theta$.
e.g., $\theta=\frac{\lambda}{d}$

now if width of slit is doubled then size of central Angular width of central Maxima will be half.

while intensity becomes four times because we know intensity is inversely proportional to area. e.g., $I\proto\frac{1}{A}$
but we also know area is directly proportional to square of size(diameter).
so, intensity is inversely proportional to square of size (diameter).
so, intensity will be four times when size will be half .