(Advanced) The derivation of the diffraction equation depends on matching wave crests along the grating surface with openings in the grating. In the diagram at the right, the arrows indicate ray directions and the dashed lines are wave crests. Add a surface-normal line to the diagram and mark the diffracted angle on the diagram. Also sketch the right triangle sharing a hypotenuse with the grating spacing that can be used to derive the diffraction equation.

Three experiments involvong thin soap film(in air) are shown below. The index of refraction of the soap film is 1.25 and there is air above the soap film. In experiment I and III there is air below the soap film but in Experiment II there is glass (with index of refraction of 1.5) below the soap film. In all three expeiments the incident of light is nearly normal to the surface and has a wavelegnth of 250 nm in air. Note that the film thickness in each experiment is written on each diagram. a. What is the wavelegnth of the incident light while it is in the soap film? b Which of these three experiments will produce constructive interference as seen by the observer (i.e. the eye)?

Keeping the slit width and screen distance constant, how does the light colour such as blue, red and green affects the fringe spacing. Briefly explain your answers in words

Please answer A, B, C, D, and E.   Consider the interference pattern from a double-slit arrangement as shown. The questions and diagram are attached in images.