A student investigates how the position of the first dark band produced by a single…
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Waves Sound and Physical Optics · Waves Sound and Physical Optics
Problem
A student investigates how the position of the first dark band produced by a single narrow slit depends on the width of the slit. A laser with wavelength 550nm illuminates the slit, and a screen is placed 2.0m away. By slowly adjusting an iris diaphragm, the student can vary the slit width while continuously observing the diffraction pattern on the screen.
(a) Describe qualitatively how the distance between the central bright band and the first dark band on the screen changes as the slit width is gradually reduced. Your description should reference only quantities that can be observed in the experiment.
(b) Using geometric reasoning appropriate for small angles, explain why the distance you described in part (a) is inversely proportional to the slit width. In your explanation, identify the assumptions that allow the use of any angle approximation.
(c) Identify one experimental situation in which the small-angle approximation used in part (b) would become invalid. Describe how the observed diffraction pattern would deviate from the prediction made under the approximation.