Question

1. Light of wavelength 640 nm is incident on two slits separated by 0.880 mm. An interference pattern is observed on a screen 2.20 m away.

a) Using the small angle approximation (tan θ  sinθ), find the distance between the central maximum and the first bright fringe.

b) What percent of error is made in locating of the seventh-order bright fringe if the small angle approximation is used compared to using the exact trigonometric function?

c) How does the separation between the fringes change if the wavelength of the light is doubled?

d) Using the original 640 nm light, if the viewing screen is infinitely large, what is the algebraic expression for the highest order (m) bright fringe that can be formed on the screen? Determine the highest order on the screen.

Answer 1

Ти MAXIMA 7 0 ANGULAR SEPRAZLON B&BUEEN CENTRAL & MAXIMA S GIVEN Sind mx S2L USING У GIVES - LINEAR SEPRATION SCREEN y BETWEEN CENTRAL MAXIMA. 3 DISTANCE BEWEEN CENTRAL & (1) (640x159 m) (2-20m) 0.88 x x 10-3 1.6 x 10-6 USING APPROX y = 700 a Sino FOR POSITION, EXACT = 22 22 - Y = 7.00 ſa² - 49 x 2 Y- a²-4912 Tuo 7. ERROR Ya a (10.88 mm² - 49 (640x10 mm lume (0.88 mm) 0001292 GENERAL SEPRATTON INCREASE 0 USING SMALL APPROX. SE PRAZLON BECOMES DOUBLE d) USING AT HIGHEST ORDER m (Sin 90) = a/ 0.88 mm 1375 640x10 a > m (max)