I keep getting this one question wrong on my homework and I can’t see why

Question

The wavelength of the laser beam used in a compact disc player is 663 nm. Suppose that a diffraction grating produces first-order tracking beams that are 1.18 mm apart at a distance of 3.46 mm from the grating. Estimate the spacing between the slits of the grating (in m).

You Answered

I answered: 2.05

correct answer: 3.94

helpful hint given: First, find the angle using the tangent:

Then use it to calculate the spacing (d):

Where m=1.

Remember to convert to m (1 m = 10^-6 m)

Answer 1

For diffraction grating the bright spots are:

dsin(𝜽) = m𝝀 = 𝝀 (this is because m = 1)

Since we want the first order brights. Solve for the grating spacing

d = 𝝀 sin(𝜽)

We need the angle now. Tangent is

𝐭𝐚𝐧(𝜽) = 𝒚 / 𝑳 = (s / 2) / L

Now we need the angle between bright and central maximum. Basically, we need half spacing.

𝜽 = tan^-1 [ (s / 2) / L ]

= tan^-1 ((1.18 / 2) ⁄ 3.46)

𝜽 = 9.68°

Now just solve for spacing

d = 𝝀 sin(𝜽) = (663 x 10^-9) / sin(9.68°) = 3.93 x 10^-6 m

Note: (off by a slight fraction because of rounding)