Question

Glass catfish, tropical fish popular with hobbyists, have no pigment, and matching of the index of refraction of their tissues leaves them largely transparent-you can see through them. When a beam of white light illuminates these fish, diffraction of light from evenly spaced striations in muscle fibers produces a rainbow pattern (Figure 1). As the muscles contract, the striations get closer together, and this affects the diffraction pattern. This phenomenon has been used to study muscle contraction in living fish as they swim. Investigators set up a chamber with moving water where the fish swam steadily to stay stationary. The investigators then passed a beam of laser light of wavelength 632 nm through the fish's muscle tissue as it swam. Muscle action produced periodic changes in the distances between striations, which ranged from 1.87 to 1.94 μm. Investigators measured the change of position of a bright spot corresponding to m = 1 on a screen. If the screen was 30 cm behind the fish, what was the distance spanned by the diffraction spot as it moved back and forth? The screen was in the tank with the fish, so that the entire path of the laser was in water and tissue with an index of refraction close to that of water. The properties of the diffraction pattern were thus determined by the wavelength in water.

Answer 1