FIGURE CP33.74 shows light of wavelength incident at angle on a reflection grating of spacing

FIGURE CP33.74 shows light of wavelength λ incident at angle ϕ on a reflection grating of spacing d. We want to find the angles θ_mat which constructive interference occurs.

a. The figure shows paths 1 and 2 along which two waves travel and interfere. Find an expression for the path-length difference Δr = _r2 - r₁.b. Using your result from part a, find an equation (analogous to Equation 33.15) for the angles θ_m at which diffraction occurs when the light is incident at angle ϕ. Notice that m can be a negative integer in your expression, indicating that path 2 is shorter than path 1.c. Show that the zeroth-order diffraction is simply a ??reflection.?? That is, θ₀ = ϕ.d. Light of wavelength 500 nm is incident at ϕ = 40? on a reflection grating having 700 reflection lines/mm. Find all angles θ_m at which light is diffracted. Negative values of θ_m are interpreted as an angle left of the vertical.e. Draw a picture showing a single 500 nm light ray incident at ϕ = 40? and showing all the diffracted waves at the correct angles.

Transcribed Image Text:

Incident Diffracted wave front wave front P. Reflection grating Incident Diffracted wave front wave front Close up FIGURE CP33.74 d