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PRACTICE – Interference and Diffraction – BLANK
Problem 1 A lasers with wavelength of 550nm is incident on a 3 slit grating. The distance between two neighboring slits is 6μm. Observing the interference pattern after the light has passed through the grating, one finds that the first diffraction minimum has an angular position of 20º. a) What is the position of the second order interference maximum? b) What is the distance between the central interference maximum and the second order interference maximum on a screen 3m away from the slits? c) What is the angular position of the fifth interference minimum? d) What is the width of the slits in the grating? We now illuminate a grating with N slits – with the same distance of 6μm between two neighboring slits – with the same laser of 550nm and a second one of 555nm. e) Find the minimum number N of slits in the grating so that the first order maxima of the interference patterns of the two lasers are resolvable.
Light of wavelength 445nm is incident on a 4 slit grating. Observing the interference pattern after the light has passed through the grating, one finds that the second order maximum has an angular position of 8.5º, while the first diffraction minimum has an angular position of 10º. a) What is the distance between the centers of two neighboring slits in the grating? b) What is the width of the slits in the grating? c) What is the angular position of the sixth interference minimum? d) Below draw how the intensity of the interference pattern depends on the angular position with respect to the zeroth order maximum centered at 0º. ! e) What is the highest order, i.e. the m-th order maximum with the highest “m”, observable for this wavelength? The higher order is at angular position of 90º f) If one placed a screen 2m away from the grating, what would the distance between the second order maximum and the first diffraction minimum be? –15° –10° –5° 0° 5° 10° 15° Angular position Intensity
The picture below represents the angular dependence of the intensity of the interference profile of light of wavelength 800nm that went through a grating. ! By looking at the picture: a) Determine the number of slits in the grating. b) By reading the graph, approximately, determine the distance between the slits c) By reading the graph, approximately, determine the width of one slit. d) Draw the envelope to the interference pattern due to diffraction. Clearly label the envelope. e) Draw the envelope to the interference pattern due to diffraction if the wavelength of the light is increased. Clearly label the new envelope. –15° –10° –5° 0° 5° 10° 15°
Angular position Intensity (normilized)
A parallel laser beam of monochromatic light of wavelength 400nm, hits a grating made of 3 slits. The distance between the centers of the slits is 10μm. a) Find the angular position of the first order interference maximum. b) Find the angular position of the 2nd interference minimum. c) Find the angular position of the 5th interference minimum. d) Find the angular position of the first diffraction minimum due to the finite width of the slits. Assume that the slits width is 450nm. e) Looking at the interference pattern on a screen placed at a distance of 0.5m from the grating, what is the distance between the central interference maximum and the first diffraction minimum due to the finite width of the slits - the angular position of which you already found in part d?
A lasers with wavelength of 550nm is incident on a grating with an unknown number of slits. After observing the interference pattern formed as light passes through the grating, the data in the table are collected. Referring to them, answer the following questions. a) What is the distance between two neighboring slits in the grating? b) What is the number of illuminated slits? c) Calculate the position of the sixth interference minimum. d) What is the width of the slits in the grating? e) What is the width of the central diffraction peak on a screen 3 m away from the grating? 1st order interference maximum 5.26º 2nd order interference maximum 10.56º 3rd order interference maximum 15.96º 1st interference minimum 1.05º 2nd interference minimum 2.10º 3rd interference minimum 3.15º 1st diffraction minimum 20º 2nd diffraction minimum 43º
f) In the graph below, draw how the intensity of the interference pattern depends on the angular position with respect to the central interference peak. ! Let’s replace the grating with a new one with 80 slits and a distance of 6μm between neighboring slits. We illuminate this new grating with the 550 nm laser, and now also with a second laser that has a larger but unknown wavelength. If we observe that the third order interference maxima from the two lasers are at the limit of being resolvable (distinguishable) ... g) ... what is the wavelength of the second laser? –40° –30° –20° –10° 0 ° 10 ° 20 ° 30 ° 40 ° Angular position Intensity (not in scale)
Problem 9 Spring 2018 Exam 3 An interference pattern with angular intensity profile as given in the picture below, is obtained using a lasers with a wavelength of 550nm, and a grating with unknown distance between the slits, unknown width of each slit, and unknown number of slits. ! a) Find the numerical value of the distance between two neighboring slits in the grating. b) Find the numerical value of the width of the slits. c) What is the number of illuminated slits? Justify your answer for credit. d) Calculate the angular position of the first interference minimum. e) Calculate the angular position of the seventh interference minimum. f) What is the width of the central interference peak on a screen 3m away from the grating? –12.71º –7.90º –3.94º 0º +3.94º +7.90º +12.71º^ θ (not in scale) Intensity
