Diffraction?

Question

Please show me how to do this problem:

A diffraction grating has 10000 slits per inch. White light is diffracted through it.
-At what angle will blue light (400 nm) be observed in first order diffraction?
-At what angle will red light (750 nm) be observed?
-If this rainbow were displayed on screen 3m from the grating, what distance would the rainbow span on the screen?

Thanks!!!

Answer 1

a sin(Ang)=m lambda
where
m is an integer that labels the order of each minimum ,
lambda is the wavelength,
a is the distance between the slits
and Ang is the angle for destructive interference

m=1
b=10000/(1 inch x 25.4mm/in/1000mm/m)= 10e7/25.4
a=1/b=2.54 e -6 meter or 2.54um

angle=ArcSin(lambda/a)=
for blue light angle = ArcSin(400 nm/2540nm)= 9.06 degrees

for red light angle = ArcSin(750 nm/2540nm)= 17.17 degrees

Imagine two triangles that share the same base of 3 m. one has an angle of 9.06 deg and the other 17.17 deg.
The difference in height of these triangles is the span of the rainbow.

Delta h= h2-h1 and tan(Ang1)=h1/base
Delta h= base (tan(Ang2)- tan(Ang1))=
Delta h=3(tan(17.17)- tan(9.06))=
Delta h=.45m