The angular position θm of the first minimum is determined by the equation sinθm=λ/d, where λ=725×10−9m is the wavelength, and d=18.5×10−6m is the width of the slit. We obtain sinθm=0.725/18.5≈0.0392. In view of the smallness of this number, we have sinθm≈θm≈0.0392. The angular width of the central maximum is twice this angle: θ=2θm≈0.0784. The angular width in degrees is then 360θ/2π≈4.5∘. The width in centimetres is proportional to the distance to the screen R=125cm and is given approximately by θR=0.0784×125cm=9.8cm.
Answer: (a) 4.5∘, (b) 9.8cm.
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