To illustrate one of the ideas of holography in a simple way, consider a diffraction grating with slit spacing d. The small-angle approximation is usually not valid for diffraction gratings, because d is only slightly larger than λ, but assume that the λ/d ratio of this grating is small enough to make the small-angle approximation valid.
a. Use the small-angle approximation to find an expression for the fringe spacing on a screen at distance L behind the grating.
b. Rather than a screen, suppose you place a piece of film at distance L behind the grating. The bright fringes will expose the film, but the dark spaces in between will leave the film unexposed. After being developed, the film will be a series of alternating light and dark stripes. What if you were to now “play” the film by using it as a diffraction grating? In other words, what happens if you shine the same laser through the film and look at the film’s diffraction pattern on a screen at the same distance L? Demonstrate that the film’s diffraction pattern is a reproduction of the original diffraction grating.