Solve Diffraction Grating Homework: 500 nm, 1st Order, 20o Angle

[physgrl]

Homework Statement

A beam of monochromatic light of wavelength 500 nm falls normally on a diffraction grating. What is the spacing between slits on the grating if a first order maximum is observed at 32o?

a. 2.88 m
b. 0.944 m
c. 0.750 m
d. 0.500 m
e. 0.250 m

Homework Equations

d=mλ/sinθ

The Attempt at a Solution

m=1 (first order)
λ=500nm
θ=32

d=1*500nm/sin(32)
d=9.44x10^-7m

the answer key says it is a) 2.88m
can anyone explain why?


I am having the same problem with:
A beam of light with a wavelength of 500 nm falls normally on a diffraction grating. What is the spacing between slits on the grating if a first order maximum is observed at 20o?

a. 171 nm
b. 500 nm
c. 1000 nm
d. 1460 nm

where I am getting 1460nm with the same procedure as above but the answer key says 1000nm :/

thanks in advance!

 

[technician]

using the figures you have given I get exactly the same answers as you.
the answer grid is wrong

 

[physgrl]

thank you! :)