An apparatus similar to the one used in this week\'s diffraction grating experim

Question

An apparatus similar to the one used in this week's diffraction grating experiment is used to measure ruling density of a diffraction grating. A second order maximum is observed to be 4.335 m from the central maximum. The wavelength of the coherent, monochromatic light striking the grating is 439 nm. The distance from the double slit to the display screen is 1.93 m.

What is the slit spacing of this diffraction grating?
Answer: 9.61×10-4 mm

What is the ruling density of this diffraction grating?

I can't seem to figure out the answer for the second question and the units that lon capa will accept. Thanks in advance!

Explanation / Answer

Formula of ruling density is given as

N = sin( theta) / m( lambda) ............1

N = rulling density

theta = angle

m = order of fringe

lambda = wavelenth

Angle ( theta) could be found by using tan relationship

tan (theta) = y / D

here y = distance of second order maximum from centeral maximum.

D = Distance between slit and screen

theta = arctan Y /D = arctan 4.335 / 1.93 = 66.070

putting in above equation 1

   N = sin 66 / 2(439)(10-9)

   N = 75255335 lines/ m

   N = 7.5 * 107 lines / m

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