# Diffraction Barrier-Class of Maximum?

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1. Jun 14, 2017

### Techno_Knight

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

tanθ = y/L
sinθ = m*λ/d

3. 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!

Last edited: Jun 14, 2017
2. Jun 14, 2017

### BvU

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

3. Jun 14, 2017

### Techno_Knight

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