40. || Helium atoms emit light at several wavelengths. Light from a helium lamp illuminates a diffraction grating and is observed on a screen 50.00 cm behind the grating. The emission at wave- length 501.5 nm creates a first-order bright fringe 21.90 cm from the central maximum. What is the wavelength of the bright fringe that is 31.60 cm from the central maximum?

You shine an orange laser (638 nm) on a double slit in an experiment you perform in your physics lab. Measuring with a protractor you see that the interference pattern makes the first fringe at 20.0° with the horizontal. What is the separation between the slits? Additional Materials |Reading

4. A single slit of width 0.21 mm is illuminated with monochromatic light of wavelength 635 nm, and a diffraction pattern is formed on a screen 2.00 m away from the slit. What is the width of the bright fringe adjacent to the central maximum? cm

1. A diffraction grating has N lines per centimeter and is placed 2.19 m away from a screen. Sunlight shines on the diffraction grating, incident along the normal, and we observe the spectrum of the sun, where light of many wavelengths are separated on the screen. We see the 1st order appearance of the Halpha line (656.28 nm) at a position 11.5 cm away from the central maximum. a) How many lines per centimeter does this diffraction grating have? N = ________________________ b) How far (in cm) from the central maximum would the first-order H-gamma line (434.0472 nm) appear? ________________________ c) What is the angular separation between the second-order H-alpha and H-gamma lines? ________________________ d) Find the wavelength(s) of visible light that would have maxima at a point on the screen 37.4 cm from the central maximum?

b) In a Young’s double-slit experiment, the slit separation and slit-screen distances are0.024 cm and 1.8 m, respectively. In the experiment, a seventh-order dark fringeoccurred at a distance of 3.5 cm from the central maximum. Calculate the:i) wavelength of light used,ii) distance between adjacent fringes, andiii) diffraction angle of the seventh-order dark fringe.

. Two narrow slits are separated by a distance of 1.2x 10-4 m. They are illuminated by the light from a sodium lamp having wavelength of 589 nm. Calculate the angular position of the first-order maximum in the interference pattern. If the light is intercepted by a photographic film placed at a distance of 2 m from the slits, calculate the distance between the resulting maximum and the central maximum on the film.

Light of wavelength A = 545 nm passes through a pair of slits that are 33 um wide and 215 µm apart. How many bright interference fringes are there in the central diffraction maximum? How many bright interference fringes are there in the whole pattern? |

2)A new experiment is created with the screen at a distance of 1.9 m from the slits (with spacing 0.09 mm). What is the distance between the second order bright fringe of light with λ = 681 nm and the third order bright fringe of light with λ = 414 nm? (Give the absolute value of the smallest possible distance between these two fringes: the distance between bright fringes on the same side of the central bright fringe.) |x| =

Problem 4 | The full width at half maximum (FWHM) of the central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (a) Show that the intensity drops to one-half of the maximum value when sin² a = a²/2. (b) Verify that a = 1.39 radians (about 80°) is a solution to the transcendental equation of part (a). (c) Show that the FWHM is A0 = 2 sin ¹ (0.443\/a). (d) Calculate the FWHM of the central maximum for slits whose widths are 1.0, 5.0, and 10 wavelengths.

1. At what angle is the first-order maximum for 469 -nm wavelength blue light falling on double slits separated by 0.06 mm? Angle: O