---
title: "Total lines on a grating"
subject: "Engineering Physics"
chapter: 4
key: "semester_1/engineering_physics:grating-total-lines-second-order"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/grating-total-lines-second-order
site: BCT Engineering
---

# Total lines on a grating

Engineering Physics · Chapter 4: Physical Optics

- Asked in: 2069 Chaitra, 5 marks
- Video: [Diffraction Grating Problems - Physics](https://www.youtube.com/watch?v=gf7j2fumz70) — The Organic Chemistry Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/grating-total-lines-second-order
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-4

## Question

A diffraction grating 3cm wide produces the second order at 33° with light of wavelength 600nm. What is the total number of lines on the grating?

## Short answer

Grating element d = nλ/sinθ = 2×6×10⁻⁷/sin33° ≈ 2.20×10⁻⁴ cm. Lines per cm = 1/d ≈ 4539, total lines on 3 cm ≈ 1.36×10⁴.

## Answer

A diffraction grating obeys the grating equation (a + b) sin θ = nλ, where (a + b) is the grating element (distance between two adjacent slits) and n is the order. The total number of lines is the width divided by the grating element.

**Given:** width = 3 cm, n = 2, θ = 33°, λ = 600 nm = 6 × 10⁻⁷ m.

**Step 1: grating element**
```text
(a + b) = nλ / sin θ
        = 2 × 6×10⁻⁷ / sin 33°
        = 1.2×10⁻⁶ / 0.5446
        = 2.203×10⁻⁶ m = 2.203×10⁻⁴ cm
```

**Step 2: lines per cm**
```text
N per cm = 1 / (a + b) = 1 / 2.203×10⁻⁴ ≈ 4539 lines/cm
```

**Step 3: total lines on 3 cm**
```text
N = 4539 × 3 ≈ 13 616
```

**Answer: the grating has about 1.36 × 10⁴ lines in total (about 4539 lines per cm).**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The grating equation is:
   A. (a + b) sin θ = nλ
   B. (a + b) cos θ = nλ
   C. (a + b) = nλ sin θ
   D. (a + b) sin θ = λ/n
   Answer: A. The grating element (a+b) times sin θ equals nλ for a maximum of order n. (Key point: Grating equation)

2. For n = 2, θ = 33°, λ = 600 nm, (a + b) is about:
   A. 2.2×10^-6 m
   B. 2.2×10^-5 m
   C. 6.5×10^-7 m
   D. 1.1×10^-6 m
   Answer: A. 1.2×10^-6 / 0.5446 = 2.203×10^-6 m. (Key point: Grating element)

3. Lines per cm equals:
   A. (a + b) in cm
   B. 1/(a + b) in cm
   C. n/(a + b)
   D. (a + b) × width
   Answer: B. 1/(2.203×10^-4 cm) ≈ 4539 lines/cm. (Key point: Lines per cm)

4. The total number of lines on the 3 cm grating is about:
   A. 4539
   B. 13 600
   C. 1 500
   D. 45 390
   Answer: B. 4539 × 3 ≈ 13 616. (Key point: Total lines)

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