A research team uses a single slit of width 0.040mm at the bottom of a transparent tank filled with water (index of refraction 1.33). A laser of unknown wavelength shines upward through the slit, producing a diffraction pattern on a screen 1.20m above the slit, still inside the water.
The measured separation between the first dark bands on opposite sides of the central maximum is 24.0mm. Small angles may be assumed.
(a) Derive an expression for the vacuum wavelength of the laser light in terms of the measured separation Δy between the symmetric first dark bands, the slit width, the screen distance, and the index of refraction of the medium.
(b) Using the given data, calculate the wavelength of the light while it travels in the water.
(c) Determine the vacuum wavelength of the laser.
(d) After the tank is drained (air replaces the water), predict the new separation between the first dark bands on opposite sides of the central maximum, keeping all other distances unchanged.
(e) Discuss two conditions under which the small-angle approximation used in parts (a)–(d) would fail for this setup.