Diffraction by single slit - effect of increasing the slit width

[physicsilliterate]

For diffraction by a single slit, what is the effect of increasing (a) the slit width, and (b) the wavelength? It was a problem on my daughter's final and I never seemed to be able to answer it for her.

 

[quasar987]

The answer lies in the fact that the minima are located at intervals of $n\lambda / D$ (value of sin)... so a bigger slit (D) makes narower maxima and a larger wavelenght ($\lambda$) makes wider maxima.

 

[geosonel]

For diffraction by a single slit, what is the effect of increasing (a) the slit width, and (b) the wavelength? It was a problem on my daughter's final and I never seemed to be able to answer it for her.

for single-slit diffraction, the condition for MINIMUMs is:

$$y \ = \ \frac{m \lambda D}{s}$$

where y is the distance from central max to the m-th minimum of the diffraction pattern, m a positive integer, λ the wavelength, D the distance between single-slit and distant observation screen where diffraction pattern will be observed, and s the single-slit width. Thus:
a) increasing single-slit width will decrease width of central max ("shrink the diffraction pattern");
b) increasing wavelength will increase width of central max ("expand the diffraction pattern")