Question

I know the equation but I am just confused on one point, the answer is D (In attached file)
but how do you get it this way?
Here's what I did:

Answer 1

I used the formula : \[d \sin \theta = n \lambda\]

Then I know that N= 300 lines per mm
And Wavelength = 450 \[\times 10^-9 m\]
And when I substituted, I got 7.4 .... So I tried multiplying it by 2, (Idk why I did that).. only then I got = 14.8 = 15 !!!! (The correect ans)
So why... whhy X2?? or is there a better way of solving this question!?
Thanks in advance.

Answer 2

d= 3.33* 10^-6.
thus n = 7.4 = 7 n is an integer.
n = 0,1,-1,2,-2,...,-7
n= 15.
http://openstudy.com/study#/updates/4f9d09a1e4b000ae9ed1d3b3

Answer 3

Aw thanks yeah that makes sense but what I don't get is why is d= 3.33X 10^-6
I mean it says 300 only in the question?
Thanks :)
@Catch.me

Answer 4

Like I got everything else but how did 300 become 3333.0? :

Answer 5

450 nm = 450*10^-6 mm = 4.5 * 10^-4 mm


4.5 10^-4
--------- = 1.5 10^-6
3 10^2

not sure if this is a good approach or not

Answer 6

Thanks @Catch.me and @amistre64
:))

Answer 7

@MonsterIsEnergy he said 300 lines/ mm in grating
you need d which is the slit separation.
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/gratcal.html

thus d = 10^-3 / 300 = 3.333*10^-6.

Answer 8

Thanks a lot :)) I get it now.