Question

Light of frequency f illuminating a long narrow slit produces a diffraction pattern. (a) If we switch to light of frequency 1.3f, does the pattern expand away from the center or contract toward the center? (b) Does the pattern expand or contract if, instead, we submerge the equipment in clear corn syrup?

Short answer

1. The pattern contracts.
2. The pattern contracts.

Step-by-step solution

The given data

Light of frequency f illuminating a long narrow slit produces a diffraction pattern.

Concept and Formula used

For a single-slit experiment,

$\alpha \sin \theta =m\lambda$where $m=1, 2, 3,...$ (minima)

Here, $\lambda$is wavelength.

Increasing the frequency of the light will result in larger values of wavelength.

Observe if pattern will expand or contract with increase in frequency

(a)

If the frequency is increased to 1.3f from f, then wavelength will increase as increasing the frequency of the light will result in larger values of wavelength.

So wavelengths are higher.

Also from the equation given above, wavelength and the angles to the minima $\theta$are inversely proportional. Increasing the wavelength will decrease the angles to the minima.

This will result in more tighter and hence contracted pattern

Rank according to up-down spreading

(b)

On submergence of experiment in corn syrup, the light would go through a material with a higher index of refraction.

So, all the light will bend in a direction perpendicular to the slit.

This results in contracted pattern.