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When coherent electromagnetic waves with wavelength \(\lambda = 120 \, \mu\text{m}\) 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.

a. 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 \(\lambda = 120 \, \mu\text{m}\)?

Answer :

Final answer:

The wavelength of the incident wave that would result in the width of the central maximum being doubled would be twice the original wavelength, i.e., 240µm.

Explanation:

In the case of electromagnetic waves incident on a single slit, the width of the central maximum is directly proportional to the wavelength of the incident wave. This means that if the width of the central maximum is doubled (from 90.0 cm to 180.0 cm), the wavelength of the incident waves should also be doubled. Therefore, if the original wavelength λ was 120μm, the new wavelength that would result in a central maximum of 180.0 cm would be 2*120μm = 240μm.

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