Red laser light of wavelength 664 nm is sent through a double-slit apparatus. Th

Question

Red laser light of wavelength 664 nm is sent through a double-slit apparatus. The slits are separated by a distance of 0.120 mm and the screen is located 2.75 m from the slits. (a) What is the angle of the 3^rd-order bright fringe? (b) What is the distance between the central bright fringe and the 3^rd-order bright fringe? Answers: (a) 0.951 degree (b) 0.0456 m or 4.56 cm For the apparatus above, find the width of the central bright fringe. Answer: 1.52 cm For the apparatus above, imagine changing the red laser for a different colored laser. Suppose the distance from the 3^rd-order fringe is now 3.14 cm. (a) What is the angle of the 3^rd-order fringe? (b) What is the wavelength of the new laser? (c) What is the color of the new laser? Answers (a and b only): (a) 0.654 degree (b) 457 nm

Explanation / Answer

1) a) Here, d * sin(theta) = n * lambda

=> 0.120 * 10-3 * sin(theta) = 3 * 664 * 10-9

=> angle = 0.951 degree

b)   distance between central and 3rd order =   2.75 * tan0.951

                                                                 =   0.0456 m

2)   here,   0.120 * 10-3 * sin(theta) = 1 * 664 * 10-9

=> angle = 0.317 degree

=> width of central bright fringe = 2.75 * tan0.317

                                                     = 0.0152 m

                                                     = 1.52   cm

3) a) Here,   angle = tan-1(0.0314/2.75)

                                 = 0.654 degree

    b)     0.120 * 10-3 * sin(0.654) = 3 * lambda

=>   wavelength = 457 nm

c)   color of new laser =    blue laser

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