Question

Light of wavelength lambda and frequency f passes through a single slit of width a. The diffraction pattern is observed on a screen a distance x from the slit. Winch of the following will decrease the width of the central maximum? Decrease the slit width; decrease the frequency f of the light; decrease the wavelength lambda of the light; decrease the distance x of the screen from the slit. In each case justify your answer.

Answer 1

The width of the central maxima is, \(\Delta y=\frac{2 \lambda}{d}\)

Here, \(\lambda\) is the wavelength of the light used. xis the distance between slit and screen and \(d\) is the slit width

(a) Decrease in slit witdth increases the width of the central maxima as \(\Delta y \infty \frac{1}{d}\)

(b) Since wavelength and frequency are inversly preoprtional to eacc other. Decrease in frequency increases the width of the central maxima as \(\Delta y<0, \infty \frac{1}{f}\)

(c) Decrease in wavelength decreases the width of the central maxima as \(\Delta y \cos\)

(d) Decrease in distance between slit and screen decreases the width of the central maxima as \(\Delta y \cos x\)

Thus, the comect options are \((c)\) and \((d)\)