What values exactly do I use to calculate lamba in the last column? i.e. what is

Question

What values exactly do I use to calculate lamba in the last column? i.e. what is my 'd' and 'm' values? Mille 04. I Grating d -IL- 100 lines/mmm imm/100 Xi 44 0. ool183. 85 x2 28. 8,235 7.7 x3 11.7 300 lines/mmm 1mm/300 X1 43.6 0,0085s 43.5 ,00355 X2 28. 8 0o136 37. 600 lines/mm 1mm/600 87.3 0,00733 8 89.810.00 733 X2 248.4 | 0, 020 3 49.3 Questions: Describe the differences observed in the diffraction patterns for the three gratings. . Show that Eq. (2) is (or is not) a valid approximation when L>x

Explanation / Answer

d is the spacing between the slits. So, for the first grating, i. e 100 lines/mm , there are 100 spacings (one after each line) within a width of 1 mm. So, d = (1/100) mm = 0.01 mm = 10-5 m . That is what is given in the second column.

Similarly, for the second grating d is given as d =(1/300) mm = 3.333333 x 10-3 mm = 3.333333 x 10-6 m

and for the third grating d is given as d = (1/600) mm = 1.6666667 x 10-3 mm = 1.66667 x 10-6 m

and m is just the order of the diffraction maximum. m = 1,2,3,4 .....

each grating has 3 values recorded. So, use m = 1,2,3

Just use the subscript of x or as m. for example for second order (second one in each grating) subscript of 2 is 2. so, m =2.

Just as a sample calculation,

The first order of the first grating: tan 1 = X1 /L = 14.4 / 213.8 = 0.067352666

1 = tan-1 (X1 / L) = tan-1 ( 0.067352666 ) = 3.853204 degrees

= dm/m

here m =1 (the sample calculation we are doing is for the first order maximum of the first grating)

so, = (dSin1 ) /1 = 10-5 Sin 3.853204 / 1 = 6.72004 x 10-7 m ~ 672 x 10-9 m ~ 672 nm

# sample calculation 2 :

The second order of the third grating: tan 2 = X2 /L = 248.4 / 213.8 = 1.161833489

2 = tan-1 (X2 / L) = tan-1 ( 1.161833489) = 49.28114071 degrees

= dm/m

here m =2 (the sample calculation we are doing is for the second order maximum of the third grating)

for third grating d = 1.66667 x 10-6

so, = (dSin2 ) /m = 1.66667 x 10-6 Sin 49.28114071 / 2 = 6.31599 x 10-7 m ~ 631 x 10-9 m = 631 nm

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