Diffraction Barrier-Class of Maximum?

[Const@ntine]

Homework Statement

A Diffraction Barrier has 4200 openings per 1cm. A screen stands 2.00 m opposite of the Barrier. Say that for a certain class m, the maximums that correspond with two different wavelengths (589.00 nm & 589.6 nm) abstain from each other by 1.54 mm. What is the value of m?

Homework Equations

tanθ = y/L
sinθ = m*λ/d

The Attempt at a Solution

Alright, we have:

λ₁ = 589.0 nm
λ₂ = 589.6 nm

λ₂ > λ₁ => y₂ > y₁ => D = 1.54 mm = y₂ - y₁

tanθ ~ sinθ [θ is a small angle)

Also, d = 1 cm/4200 = 2.38 * 10^-4m

So:

D = L*m*(λ₂ - λ₁)/d <=> m = d*D/(λ₂ - λ₁)*L <=> ... <=> m = 3

My problem is that the naswer the book gives is m = 2. I run the numbers many times, and I always get 3. Am I doing something wrong? Is there a problem in the math or the logic?

Any help is appreciated!

 

[BvU]

I find 3 just like you do. Looks as if book answer is wrong.

 

[Const@ntine]

I find 3 just like you do. Looks as if book answer is wrong.

It's been wrong before, but I wanted to make sure. Thanks a lot for the input!