When coherent electromagnetic waves with wavelength [tex]\lambda = 120 \, \mu m[/tex] are incident on a single slit of width 'a', the width of the central maximum on a tall screen 1.50 m from the slit is 90.0 cm.

For the same slit and screen, for what wavelength of the incident waves is the width of the central maximum 180.0 cm, double the value when [tex]\lambda = 120 \, \mu m[/tex]?

The width of the central maximum on a diffraction pattern is directly proportional to the wavelength of the incident wave. Therefore, when the maximum width doubles, so should the wavelength, in this case to 240μm.

Explanation:

The width of the central maximum on a diffraction pattern relates to the wavelength of light and the width of the slit through which the light passes. In this case, we have a known value for the original wavelength (λ=120μm) and we can see that the width of the central maximum doubles when the wavelength changes. This suggests that the relationship between these values is directly proportional.

So, if the wavelength doubles, the width of the central maximum should also double. Thus, for the width of the central maximum to be 180.0 cm, double that of when λ=120μm, the wavelength should also double. Therefore, the wavelength of the incident waves should be 240μm.

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