Question

Problem 7 (20 points): Each graph below shows the relative intensity versus 0 for a double slit experiment. The horizontal scale is the same for all graphs. The only possible differences among the cases are the values of the slit width (a) and distance between the centers of the slits (d). Case For each of the three cases, calculate the ratio- a) 0.5 b) Rank the cases according to distance between the centers Case 2 of the slits (d), from largest to smallest. If the distance between the centers of the slits is the same in any of the cases, state that explicitly. Please be sure to explain all of your reasoning using features of each graph. Case 3 cRank the cases according to width (a) of the slits, from largest to smallest. If the width is the same in any of the cases, state that explicitly. Please be sure to explan all 0.5 of your reasoning using features of each graph. Problem 7 (cont): d) In an experiment, green light of wavelength 500 nm is incident onto a thin single slit of unknown width a. A single-slit diffraction pattern is formed on a screen 1 m away. The first and second diffraction minima are observed to be 1 cm apart on the viewing screen. Please draw a picture of the experiment below and calculate the slit width a. (Hint: do the angles associated with the diffraction pattern qualify as small angles?) In a separate experiment, light of an unknown wavelength is incident on the same single slit as described above. A single-slit diffraction pattern is again observed on a screen 1m away, but now the first and third diffraction minima are observed to be 2.4 cm apart. Calculate the wavelength of the light used in this experiment. Is it larger, smaller, or the same as before? e Consider the Hubble Space Telescope, which has a circular aperture of diameter 2.5 m. · Calculate the minimum angular resolution (in radians) of this telescope for light at λ 500nm. Can the Hubble Space Telescope resolve the headlights of a lunar buggy on the moon? Assume the headlights are 1 m apart and use 4.0 x 10m for the telescope-moon distance. Please justify your answers, noting that the headlight separation is much, much, much smaller than the telescope-moon distance. Please also draw a diagram, labeling distance values.

Answer 1

From the Intensity vs 0 graph for the double slit experiment, the values of slit width and slit separation are shown in the following figure: Determined by slit width Determined by the separation between slits In the figure, d is the slit separation and a is the slit width (a) From the graph of case-1, the slit width is as follows a 6 units And the separation between the slits is as follows: d 3 units d for the 1st case is as follows: Hence, the ratio a d 3 units 6 units 1 2

From the graph of case-2, the slit width is as follows: a 8 units And the separation between the slits is as follows: d 3 units d for the 2nd case is as follows: Hence, the ratio d 3 units 8 units From the graph of case-3, the slit width is as follows: a 10 units And the separation between the slits is as follows: d 2 units d for the 3rd case is as follows: Hence, the ratio d 2 units 10 units 1 5 (b)

From the graph of case-1, the separation between the slits is as follows: d 3 units From the graph of case-2, the separation between the slits is as follows: d, 3 units _ From the graph of case-3, the separation between the slits is as follows: d 2 units From the above conclusions, the rank of lit separations for the three cases is d d, > d (c) From the graph of case-1, the slit width is as follows: a 6 units From the graph of case-2, the slit width is as follows: a, 8 units _ From the graph of case-3, the slit width is as follows a 10 units From the above conclusions, the rank of slit widths for the three cases is a, < a, < a