There are 5630 lines per centimeter in a grating that is usedwith light whose wa

Question

There are 5630 lines per centimeter in a grating that is usedwith light whose wavelegth is 473 nm. A flat observation screen islocated 0.788 m from the grating. What is the minimum width thatthe screen must have so the centers of all the principalmaxima formed on either side of the central maximum fall on thescreen? I got an answer of 47.01m after following the cramstertutorial but it is wrong and I can't see how it's wrong There are 5630 lines per centimeter in a grating that is usedwith light whose wavelegth is 473 nm. A flat observation screen islocated 0.788 m from the grating. What is the minimum width thatthe screen must have so the centers of all the principalmaxima formed on either side of the central maximum fall on thescreen? I got an answer of 47.01m after following the cramstertutorial but it is wrong and I can't see how it's wrong

Explanation / Answer

   wavelength = 473 nm
                       = 473 x 10-9 m
   the last maxima will be at = 90o
   L = 0.788 m
   if a is the slit width then from the theory we havethe equation
   a sin = m
   m = (a / ) sin
       = (a / )sin90o
   a = (1 / 5630 lines per cm)
      = 1.77 x 10-4 cm
      = 1.77 x 10-6 m
   so we get
   m = (1.77 x 10-6 m / 473 x10-9 m)
       = .........
   after gettimg the value of m, the angle correspondingto m will be
   = sin-1(m / a)
      = ...........o
    from the theory we have the equation
   y = L tan
   the screen must have a width of 2 y = ................m
   hope you got it

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