21. Light From a Helium-Neon lase (2-632.8 nm) is incident normally on diffraction grading containing 6000 grooves per centimeter. Find angles at which the first and second order maxima are observed. 22. A light source emits visible light of two wavelengths: 1=430 nm and (A1=510 nm). The source is used in a double-slit interference experiment in which L=1.5 m and d=0.025 mm. Find the separation distance between the third-order bright fringes for the two wavelengths.

21. Light From a Helium-Neon lase (2-632.8 nm) is incident normally on diffraction grading containing 6000 grooves per centimeter. Find angles at which the first and second order maxima are observed. 22. A light source emits visible light of two wavelengths: 1=430 nm and (A1=510 nm). The source is used in a double-slit interference experiment in which L=1.5 m and d=0.025 mm. Find the separation distance between the third-order bright fringes for the two wavelengths.

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter30: Atomic Physics

Section: Chapter Questions

Problem 53PE: (a) What is the distance between the slits of a diffraction grating that produces a first-order...

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Show that the distribution of intensity in a double-slit pattern is given by Equation 36.9. Begin by assuming that the total magnitude of the electric field at point P on the screen in Figure 36.4 is the superposition of two waves, with electric field magnitudes E1=E0sintE2=E0sin(t+) The phase angle in in E2 is due to the extra path length traveled by the lower beam in Figure 36.4. Recall from Equation 33.27 that the intensity of light is proportional to the square of the amplitude of the electric field. In addition, the apparent intensity of the pattern is the time-averaged intensity of the electromagnetic wave. You will need to evaluate the integral of the square of the sine function over one period. Refer to Figure 32.5 for an easy way to perform this evaluation. You will also need the trigonometric identity sinA+sinB=2sin(A+B2)cos(AB2)
In Figure P36.10 (not to scale), let L = 1.20 m and d = 0.120 mm and assume the slit system is illuminated with monochromatic 500-nm light. Calculate the phase difference between the two wave fronts arriving at P when (a) = 0.500 and (b) y = 5.00 mm. (c) What is the value of for which the phase difference is 0.333 rad? (d) What is the value of for which the path difference is /4? Figure P36.10
(a) Find the angle between the first minima for the two sodium vapor lines, which have wavelengths of 589.1 and 589.6 nm, when they fall upon a single slit of width 2.00 m. (b) What is the distance between these minima if the diffraction pattern falls on a screen 1.00 m from the slit? (c) Discuss the ease or difficulty of measuring such a distance.
(a) What is the distance between the slits of a diffraction grating that produces a first-order maximum for the first Balmer line at an angle of 20.0°? (b) At what angle will the fourth line of the Balmer series appear in first order? (c) At what angle will the second-order maximum be for the first line?
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