Calculate N Slit Diffraction: Grating Width 5cm, Slit 0.0001cm, λ 5.5 x 10-5cm

[Sharlom]

if I'm given grating width=5cm ,slits of width=0.0001cm separated by a distance of 0.0002cm
how many order would be observable at λ=5.5 x 10-5cm?
calculate the width of principle maximum?

please tell me the approach to do this problem

 

[Sharlom]

to find observable orders,
In the websites it said use the formula dsinθ=mλ
then keep θ=90 and find m.
but why θ is put 90 degrees I'm not able understand?

 

[Sharlom]

here is one more similar question..please clear these doubts.
How many orders will be visible if the wavelength of the incident light is 5000 Å and the number of lines on the grating is 2620 per inch?
Ans: First of all I will find distance between each slit
d=1/2620 inch=2.54/2620 cm=9.69 x 10^-4cm
keep θ=90 and find m (this i did to find the number of visible orders)
substituting values,
using the formula dsinθ=mλ
(9.69 x 10^-4 cm)sin90=m(5000 x 10^-8 cm)
I got m=19.38
# here it is coming to be a decimal number,the thing I know is that m should not come in decmals so i have a doubt that is my answer correct?
#let's say i round off 19.38 to 19 then it seems that 19 orders are visible, but imagine if m=19.6 or 19.8 etc. if this i round it off to 20,will my answer be right?
or still 19 orders are only visible ,since 0.6 or 0.8 are not an integer?

 

[Sharlom]

here is one more similar question..please clear these doubts.
How many orders will be visible if the wavelength of the incident light is 5000 Å and the number of lines on the grating is 2620 per inch?
Ans: First of all I will find distance between each slit
d=1/2620 inch=2.54/2620 cm=9.69 x 10^-4cm
keep θ=90 and find m (this i did to find the number of visible orders)
substituting values,
using the formula dsinθ=mλ
(9.69 x 10^-4 cm)sin90=m(5000 x 10^-8 cm)
I got m=19.38
# here it is coming to be a decimal number,the thing I know is that m should not come in decmals so i have a doubt that is my answer correct?
#let's say i round off 19.38 to 19 then it seems that 19 orders are visible, but imagine if m=19.6 or 19.8 etc. if this i round it off to 20,will my answer be right?
or still 19 orders are only visible ,since 0.6 or 0.8 are not an integer?

even if m comes to be 19.8 or 19.6 or 19.9 etc. it should be taken as m=19 only.thus 19 orders will be visible.

 

[jtbell]

but why θ is put 90 degrees I'm not able understand?

Imagine that you are standing right next to the slits. 0° means you are looking directly away from the slits, perpendicular to the screen that the slits are cut into. If you now turn through an angle greater than 90°, where are you looking? Can the light diffracted through the slits actually travel in that direction? (in the diagram below, the light travels from left to right)

 

[Sharlom]

Thank you..