Diffraction with Huygen's Principle Practice Problems

Using Huygens Principle, derive the law of reflection which states that the angle of incidence is equal to the angle of reflection on a smooth surface.

Imagine that you are performing an experiment to study double-slit interference patterns. You have a setup where the distance "d" between the slits is much larger than the wavelength "λ" of the light passing through them. Calculate the angular full width value at the half maximum point of the central peak in the interference pattern based on this particular setup.

Consider an experimental setup where three equally spaced and equal-intensity coherent sources of green light (L₁, L₂, and L₃) are placed in a line. Using the phasor method and phase difference $𝛿=\frac{2\pi dsin\theta}{\lambda}$, determine the relative intensity $I/I_0$ of the light at point S.

In an experimental setup, three equally spaced and equal-intensity coherent sources of red light: L₁, L₂, and L₃ are placed in a line. Using the phasor method and phase difference of $\delta$ = $\frac{2\pi\cdot d\cdot\sin\left(\theta\right)}{\lambda}$, determine the locations of the maxima "θ_max" in the interference pattern.

In an experimental setup, three equally spaced and equal-intensity coherent sources of red light (L₁, L₂, and L₃) are placed in a line. Using the phasor method and phase difference 𝛿=2πdsinθ/λ, determine the locations of the minima θ_min in the interference pattern.