A Young’s double slit apparatus has the slit separation of 0.12mm and the distan

Question

A Young’s double slit apparatus has the slit separation of
0.12mm and the distance between the slits and the viewing
screen is 55 cm.
A) If monochromatic light of wavelength ? = 550x10-9 m passes
through the slits, calculate the distance between the central
(bright) fringe and the adjacent bright fringe.
B) Now imagine that you are using X-rays, ?=1x10–9 m instead of
visible light in this experiment. What would the slit separation
need to be in order to have the distance between these first two
bright fringes be 1cm?

Explanation / Answer

A)The slit separation is d = 0.12 mm = 0.12 * 10^-3 m
The distance between the slits and the viewing screen is D = 55 cm = 55 * 10^-2 m
The wavelength of monochromatic light through the slits is ? = 550 * 10^-9 m
The distance between the central (bright) fringe and the adjacent bright fringe is ß = (m?D/d) where m = 1,
B)Let the slit separation be d1 in order to have the distance between these first two
bright fringes to be 1cm.Therefore,we get d1 = (m?D/ß) where m = 1,? = 1 * 10^-9 m and ß = 1 cm = 1 * 10^-2 m

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