Number of Visible Diffraction Orders on a Grating

[Sabrina_18]

Homework Statement

How many orders of diffraction will be visible if light of wavelength 500nm fals on a grating with 600 000 lines per metre?

Homework Equations

n = dsinѲ / λ

The Attempt at a Solution

n = 6X10⁵m ÷ 5 X 10ˉ⁷m = 1.2
So 1 order of diffraction will be visible is this right??

I don't have the angle so I could put it into the equation.

 

[Redbelly98]

Note that d is really (1/600,000) m, so that 600,000 lines would fit in 1 m.

 

[oedipa maas]

Another way to pose this question is: how many maxima do you see between theta=0 and theta=90 degrees?

Consider that for a maximum to appear on the wall or the screen in front of the grating the angle theta can never be more than 90 degrees. (Recall that sin(theta) ~ (distance of nth maxima from the 0th maxima)/(distance of the grating from the screen).)

 

[Sabrina_18]

Thanks for your help. Here is my improved answer:
λ = 500nm = 5 X 10ˉ⁷m
d = 6 X 10⁵ per metre = 1 ÷ 6 X 10⁵ = 16.7 X 10ˉ⁷m
n = 16.7 X 10ˉ⁷ X sin 90 ÷ 5 X 10ˉ⁷ = 3.34
There will be 3 orders of diffraction visible

Is this correct? If not please tell me where I am going wrong

Thanks

 

[Redbelly98]

Looks good. Problem solved