Final answer:
In single slit diffraction, the scalar summation of the electric field can be equated to the electric field at the maxima, which occurs at points where the path difference between the waves from different parts of the slit is zero. To find the electric field at the maxima, the contributions from every point on the slit need to be summed up.
Step-by-step explanation:
In single slit diffraction, the scalar summation of the electric field can be equated to the electric field at the maxima. The electric field at the maxima occurs at points where the path difference between the waves from different parts of the slit is zero. This is when constructive interference happens and the waves add up to form a maximum.
For example, consider a single slit with a width 'd'. At points where the small angle approximation is valid, the distance between the center of the slit and the point on the screen is much greater than the distance from the slit to that point. In this case, the path difference between the waves from different parts of the slit can be approximated as 'dsin(θ)', where 'θ' is the angle from the center of the slit to the point on the screen.
To find the electric field at the maxima, you would need to sum up the contributions from every point on the slit. The electric field from a single point on the slit can be given by the equation E = Eo*sin(2πx/λ), where 'Eo' is the amplitude of the electric field, 'x' is the position on the slit, and 'λ' is the wavelength of the light. Integrating this equation over the entire width 'd' of the slit would give you the total electric field at the maxima.