006 10.0 points A double -slit interference experiment is per- formed with light

Question

006 10.0 points A double -slit interference experiment is per- formed with light from a laser. The separa- tion between the slits is 0.50 mm, and the first -order maximum of the interference pat- tern is at an angle of 0.056 degree from the center of the pattern. What is the wavelength of the laser light? Answer in units of nm 007 10.0 points A double -slit interference experiment is per- formed using red light from a hydrogen dis- charge tube (lambda = 656 nm). The fifth -order bright fringe in the interference pattern is 0.749 degree from the central maximum. How far apart are the two slits separated? Answer in units of m 008 10.0 points A beam containing light of wavelengths of lambda 1 and lambda 2 passes through a set of parallel slits. In the interference pattern, the fifth bright line of the A1 light occurs at the same position as the sixth bright line of the lambda 2 light. If A1 is known to be 507.3 nm, what is the value of lambda 2? Answer in units of nm

Explanation / Answer

Diffraction condition

a sin theta = m lambda

a = 0.50 * 10-3 m, m = order of the pattern = 1 , theta = 0.0560

lambda = a sin theta / m = (0.50 * 10-3 * sin 0.056) / 1

= 4.89 * 10-7 m = 489 nm

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d sin theta = n lambda

d = (5 * 656 * 10-9) / (sin 0.749)

= 0.251 mm = 0.000251 m

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5th brigth fringe = 6th bright fringe

5D lambda1/d = 6D lambda2 / d

5 lambda1 = 6 lambda2

lambda2 = 5 lambda1 / 6 = 5 * 507.3 / 6

= 422.75 nm

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