Calculating Diffraction Grating Spacing for Red Light | Homework Help

[Hannahj1]

Homework Statement

A diffraction grating produces a third-order maximum, at an angle of 22 degrees, for red light (694.3 nm). Determine the spacing of the lines.

Homework Equations

for maxima:

sin θm = mλ/d

where m is the order of the maxima, λ is the wavelength in nm, and d is the spacing of the lines

The Attempt at a Solution

λ = 694.3 nm
θ = 22
m = 3

d = mλ / sin θ
d = 3 (694.3) / sin 22
d = 5560 nm

but the answer in the textbook is 7400 nm. what have i done wrong?

and this one:

Calculate the highest spectral order visible when a 6200-line/cm grating is illuminated with 633-nm laser light.

d = 1/6200 cm
λ = 633 nm = 6.33 x 10^9 cm
n = ?

how do i find n without θ? I'm probably missing some obvious things

 

[Student100]

Homework Statement

A diffraction grating produces a third-order maximum, at an angle of 22 degrees, for red light (694.3 nm). Determine the spacing of the lines.

Homework Equations

for maxima:

sin θm = mλ/d

where m is the order of the maxima, λ is the wavelength in nm, and d is the spacing of the lines

The Attempt at a Solution

λ = 694.3 nm
θ = 22
m = 3

d = mλ / sin θ
d = 3 (694.3) / sin 22
d = 5560 nm

but the answer in the textbook is 7400 nm. what have i done wrong?

and this one:

Calculate the highest spectral order visible when a 6200-line/cm grating is illuminated with 633-nm laser light.

d = 1/6200 cm
λ = 633 nm = 6.33 x 10^9 cm
n = ?

how do i find n without θ? I'm probably missing some obvious things

Are you sure they didn't mean 4th-order maximum?

I'll look at the second question in a few.

 

[Student100]

Are you sure they didn't mean 4th-order maximum?

I'll look at the second question in a few.

You're setting up an inequality for the second problem, what are the constraints on theta?