Maximum observable order
Because sin θ ≤ 1, the grating equation requires n ≤ d/λ. The highest observable order is the largest whole number not exceeding d/λ, so you round down, never up. The total number of maxima seen is 2n_max + 1, counting the central maximum once and each order on both sides.
n ≤ d/λ · n_max = floor(d/λ) · total maxima = 2n_max + 1What this actually means
The physical statement is that the diffracted beam cannot leave the grating at more than 90° to the normal. Beyond that angle the order simply does not exist.
Rounding is the mark. If d/λ = 2.63, then n_max = 2, not 3. Write since n must be a whole number, the maximum order is 2. Rounding up is an automatic loss.
The count then follows: orders 0, ±1, ±2 give five maxima in total. Students who answer two or five without explaining which they mean risk the mark, so state it as the central maximum plus two orders on each side.
Strictly, an order at exactly 90° grazes along the grating surface and is not observable, so if d/λ comes out as an exact integer the highest visible order is one less. Say so if the numbers work out that way.
Note this is the opposite behaviour to a double slit. A finer grating (smaller d, more lines per mm) spreads the orders further apart but gives you fewer of them.
Rounding d/λ up to the next whole number, or forgetting to double the orders when counting total maxima.
Prove it — watch it be true
- Set 600 lines per mm with λ = 633 nm and read d/λ from the panel.
- Check the order table and confirm the orders above the calculated limit are greyed out as non-existent.
- Count the visible rays and confirm the total is 2n_max + 1.