Physics

Physics

Problem

A diffraction grating has 500500 lines per millimeter and is illuminated by light of wavelength 700 nm700\,\text{nm}. Which of the following correctly identifies all non-central orders that can be observed? a) Only the first order b) An unlimited number of orders c) First and second orders only d) First, second, and third orders
Intuitive explanation

Diffraction gratings produce bright fringes only when the path-difference condition dsin⁡θ=mλd\sin\theta = m\lambda is satisfied, where mm is the order number. The key insight is that sin⁡θ\sin\theta can never exceed 1, so there's a maximum order beyond which no diffraction peaks exist. Calculate the grating spacing dd from the line density, then find the largest integer mm (positive and negative) for which ∣mλ∣≤d|m\lambda| \leq d—those are your observable orders.

Intuitive explanation

Diffraction gratings produce bright fringes only when the path-difference condition dsin⁡θ=mλd\sin\theta = m\lambda is satisfied, where mm is the order number. The key insight is that sin⁡θ\sin\theta can never exceed 1, so there's a maximum order beyond which no diffraction peaks exist. Calculate the grating spacing dd from the line density, then find the largest integer mm (positive and negative) for which ∣mλ∣≤d|m\lambda| \leq d—those are your observable orders.

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