A microwave of wavelength 2.0 cm falls normally on a slit of width 4.0 cm. The angular spread of the central maxima of the diffraction pattern obtained on a screen 1.5 m away from the slit, will be:
Question
A microwave of wavelength 2.0 cm falls normally on a slit of width 4.0 cm. The angular spread of the central maxima of the diffraction pattern obtained on a screen 1.5 m away from the slit, will be:
Solution
The angular spread of the central maxima of the diffraction pattern can be calculated using the formula for single-slit diffraction:
θ = λ / b
where:
- λ is the wavelength of the light
- b is the width of the slit
Given that λ = 2.0 cm = 0.02 m and b = 4.0 cm = 0.04 m, we can substitute these values into the formula:
θ = 0.02 m / 0.04 m = 0.5 rad
However, this is the angle for one side of the central maxima. The total angular spread would be twice this value, or 1.0 rad.
Please note that this is a simplification. The actual diffraction pattern would also depend on other factors, such as the distance to the screen and the intensity of the light. But for a basic calculation, this should give you a good estimate.
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