Width of central maximum from a single slit?

Question

The diffraction pattern from a single slit is viewed on a screen. Using blue light, the width of the central maximum is 2 cm

(b) If the blue light has wavelength 0.39 m and the red light has wavelength 0.8 m, what is the width of the central maximum when red light is used?

Answer 1

As wavelength increases, all the features of a response curve spread out because it requires a larger theta to add a wavelength of difference to the light paths. With the small-angle approximation commonly used, the width is proportional to wavelength. So the maximum at 0.8 μ = 0.8/0.39 * 2 cm.