Deriving n ≤ d/λ from sinθmax ≤ 1

[jono240]

There is a crucial aspect of this unit that I am not understanding and that is how to find how many nodal or anti nodal lines are in the equation.

relevant formulas:
So if I am looking for how many anti nodal lines exist I use the formula | dsinθmax = n*λ |

So let's say I have d and λ
d = 51cm and λ = 4

So we need to solve for n

1. Now on the board, the teacher will write the formula | dsinθmax = n*λ |

2. from there we get | sinθmax = (n*λ) / d | which cannot be greater than 1.

3. so | (n*λ) / d ≤ 1 |

4. then we get | n ≤ (d / λ) |

5. n = (51 / 4)

6. n = 12.75

then you get the answer for n.
I just don't get at all how you get from 3. to 4. algebraically
i really need this cleared up. I need to understand how that works. I hope someone can explain it to me
thanks

 

[sandy.bridge]

I'm not entirely sure if this is real, but regardless, here you go:

$$\left| \frac{n\lambda}{d}\leq1\right|$$
$$\left| \frac{n\lambda}{d}\frac{d}{\lambda}\leq \frac{d}{\lambda} \right|$$
$$\left| n\leq\frac{d}{\lambda}\right|$$