Monochromatic light is normally incident on the diffraction grating. The second-order maximum

Monochromatic light is normally incident on the diffraction grating. The second-order maximum is observed at an angle of 30 ° to the normal. What is the maximum order of the diffraction spectrum?

Given:
k = 2;
φ = 30 degrees.
Find: kn.
Decision:
In order to solve the problem, we write down the formula in which the sine will appear, since in the condition we are given an angle. The formula will look like this: d * sin φ = k * λ.
Let us express the sine from this formula. Then we get: sin φ = k * λ / d. Substitute the values ​​we know into the formula, namely the angle and k. Sin30 = 2 * λ / d
We know that the sine of 30 degrees will be 1/2, so the equation looks like: 2 * λ / d = 0.5.
Divide both sides by 2 to get rid of the numerical values ​​on the left side of the equation: λ / d = 1/4.
Next, consider the following case: sin φ≤1
. Means kn / 4≤1 and kn≤4. From these conditions, we conclude that kn can be equal to only one number, namely kn = 3.
Answer: 3