Question

Light of wavelength 550 nm is incident on a double slit with spacing d= 1 x 10-4 m and slit width a the slits. 1. 0.05 x 10.4 m. A screen is placed 1 m from (a) Find the spacing between bright lines on the screen. (You may use the small angle approximation) /2 (b) Find the distance to the first single slit diffraction dark fringe. /2 (e) What fringe number of the double slit pattern has the first dark fringe of the single slit pattern on top of it? /2 If the light is changed to 650 nm describe the difference in the resulting pattern. 2. /2

Answer 1

Light of wavelength 550 nm is incident on a double slit with spacing d = 1 times 10^-4 m and slit width a = 0.05 times 10^4m. A screen is placed 1m from the slits. Light of wave length 550 nm D = 1 times 10^-4 m Slit width a = 0.05 times 10^-4 m D = 1m the small angle approximation of the position of n^th is given by y_n = n times D/d B = y_n - y_n - 1 = lambda D/d = 550 times 10^-9 times 1/1 times 10^-4 = 5.50 times 10^-3 m The spacing Between two the small angle approximation = 5.50 times 10^-3 m find the distance to the first single slit dark a sin theta = n lambda Here n = 1 a sin theta = lambda the small angle approximation sin theta = y/D \r\n so we can find that y' ay'/D = lambda y' = lambda/D = a