EXPERIMENT 1 — THICKNESS OF WIRE
Laser Diffraction  ·  λ = 6328 Å = 632.8 nm  ·  d = Dλ/b
LASER OFF
⚙ SETUP
▸ SELECT LASER SOURCE
SELECT WIRE (d increasing →)
Screen Distance D 1000 mm
700900110013001500
Laser:—
λ:—
Wire:—
D:—
b = Dλ/d =—
⚠ TURN ON LASER TO ADD READINGS
d = D × λ / b
b = measured half-width (±2.5% noise)
Each D → different b → different d_calc
Increasing D → pattern visually spreads
Mean d = average of all d_calc
Turn ON laser to begin
b = — mm
📋 OBSERVATION TABLE
b = measured (noise)  ·  d_calc = Dλ/b after [▶ Calculate]
d = Dλ/b  ·  λ varies per laser

THEORY — UNDERSTANDING THE EXPERIMENT FROM SCRATCH

🔴 What is a Laser?

A laser is a special light source that produces light of a single colour (wavelength), travels in a perfectly straight line, and is extremely narrow. In this experiment we use a He-Ne (Helium-Neon) laser which emits red light at a wavelength of λ = 632.8 nm = 6328 Å. Because the beam is so well-defined, it is perfect for measuring tiny things like the thickness of a thin wire.

🌊 What is Diffraction?

Normally we think of light as travelling in straight lines. But when light passes very close to an edge — or is blocked by a very thin obstacle like a wire — it bends slightly around the edges. This bending is called diffraction. The amount of bending depends on the wavelength of light and the size of the obstacle.

Think of water waves: when waves pass through a small gap, they spread out on the other side. Light does exactly the same thing, just at a much smaller scale.

🔬 Babinet's Principle — Why a Wire Works Like a Slit

Here is an important idea: the diffraction pattern produced by a thin wire is identical to the pattern produced by a thin slit of the same width. This is called Babinet's Principle. The wire (an opaque obstacle) and the slit (an open gap) are complementary to each other — their patterns are the same in intensity distribution.

This is very convenient because single-slit diffraction is well understood mathematically, and we can directly apply those formulas to the wire.

💡 What Does the Pattern Look Like?

When the laser hits the wire, you see on the screen:

→ A bright central band at the centre (the central maxima)
→ Dark bands (fringes) on both sides of the bright centre — these are called minima
→ More faint bright bands beyond the dark ones (secondary maxima)
→ The pattern is symmetric on both sides

📌 b = half-width of central maxima — This is the distance from the very centre of the bright central band to the first dark band (first minimum) on either side. This is what you measure in the experiment.

📐 Deriving the Formula — Step by Step

Step 1: For a wire of thickness d, the condition for the first dark fringe (first minimum) is:

d · sin θ = λ

where θ is the angle at which the first dark fringe appears, and λ is the wavelength of light.

Step 2: In the lab, the angles involved are very small (a few degrees at most). For small angles, we can use the approximation: sin θ ≈ tan θ.

Step 3: If D is the distance from the wire to the screen, and b is the half-width of the central maxima (measured on the screen), then by geometry: tan θ = b / D.

Step 4: Substituting sin θ ≈ b/D into the condition d·sinθ = λ:

d · (b / D) = λ

Step 5: Rearranging to find d (the wire thickness):

d = D × λ / b

This is the working formula. All three quantities on the right side are measurable: D with a metre scale, λ is known (632.8 nm for He-Ne), and b from the diffraction pattern on the screen.

📏 Why Does b Change When D Changes?

From the formula b = Dλ/d, we can see that b is directly proportional to D. If you double D, b also doubles. This makes physical sense — at a greater distance, the diffracted rays have more space to spread apart, so the pattern is bigger. You can verify this directly in the simulation by moving the D slider.

📊 Intensity Distribution — The Mathematics

The complete intensity pattern across the screen is described by:

I(θ) = I₀ · (sin β / β)²    where β = π·d·sinθ / λ

When β = 0 (centre), the formula gives I = I₀ (maximum brightness). When β = π, 2π, 3π... the intensity becomes zero — these are the dark fringes. The central bright band is the widest and brightest. Each side band is progressively dimmer.

🔬 Why Do d_calc Values Vary Slightly?

In a real lab, when you measure b with a ruler, you cannot get it exactly right every single time. There is always a small reading error of ±1 to 3 mm depending on the scale. Because d = Dλ/b, even a tiny change in b gives a slightly different d_calc. This is not a mistake — it is normal experimental error. By taking readings at multiple values of D and calculating the mean, you reduce this random error and get a more reliable answer.

📌 Key Relationships Summary

• Thinner wire (smaller d) → larger b → wider pattern on screen

• Larger screen distance (larger D) → larger b → pattern spreads wider

• Longer wavelength (red vs blue laser) → larger b → wider pattern

• b vs D graph → straight line through origin, slope = λ/d → d = λ/slope

⚠️ Experimental Limitations

This experiment works only when b falls within a measurable range on the screen. Two extreme cases make measurement impossible:

↕ Case 1 — Wire Too Thin (e.g. Wire 0, d = 0.02 mm)

When d is extremely small, b = Dλ/d becomes very large. The central maxima becomes so wide that it overflows the edges of the screen completely. The first dark fringe falls outside the screen area, so b cannot be measured at any value of D.

Real-world example: A human hair (~0.07 mm) at D = 1500 mm gives b ≈ 13.6 mm — borderline measurable. A spider web thread (~0.003 mm) would give b ≈ 316 mm — totally unmeasurable on any normal screen.
● Case 2 — Wire Too Thick (e.g. Wire 6, d = 2.5 mm)

When d is very large, b = Dλ/d becomes extremely small — smaller than what the human eye or a scale can resolve on screen. The dark fringes are so closely packed that they appear as a single uniform bright spot. Individual fringes cannot be distinguished, so b cannot be measured.

Real-world example: A 1 mm copper wire at D = 1000 mm gives b ≈ 0.06 mm — far below the ~0.5 mm resolution of a normal ruler. A 2.5 mm wire gives b ≈ 0.025 mm — completely unresolvable.

In this simulation, Wire 0 (d = 0.020 mm) always falls in Case 1 and Wire 6 (d = 2.500 mm) always falls in Case 2. Selecting either and clicking [+ Add Reading] will show the limitation message in the observation table instead of a recorded value. Wires 1–5 are designed to fall within the measurable range at D = 700–1500 mm.

PROCEDURE — HOW TO DO THIS EXPERIMENT

🧪 Apparatus Required

He-Ne Laser (λ = 6328 Å) with power supply and stand · 5 thin wires of different (increasing) thicknesses mounted on holders · Optical bench (a long straight rail to keep everything aligned) · White screen with millimetre markings · Metre scale for measuring D · Dark room for clear fringe visibility

⚠️ Safety First — Read Before Starting

🚨 LASER SAFETY: NEVER look directly into the laser beam or its reflection. Even a brief exposure can permanently damage your eyes. Always point the laser away from people. Use the laser only when it is properly mounted and directed at the screen.

🔧 Real Lab Procedure — Step by Step

1
Setup the laser: Place the He-Ne laser on the optical bench. Connect to the power supply. Switch it ON and wait 5 minutes — lasers need a warm-up period to stabilise their output. After warm-up, the beam should be steady and bright red.
2
Mount Wire 1 (thinnest): Place the wire holder on the bench so the wire is exactly perpendicular (vertical, at 90°) to the laser beam. The laser beam should graze right alongside the wire. Check alignment by looking at the shadow — the wire should be centred in the beam.
3
Place the screen at D = 1000 mm: Set the white screen at a distance of 1000 mm from the wire. Measure this distance carefully with a metre scale from the centre of the wire to the screen surface. Mark this distance.
4
Observe the diffraction pattern: Turn off room lights (dark room gives clearer fringes). You will see on the screen: a bright central horizontal band in the middle, flanked by dark bands on both sides. These dark bands are the diffraction minima. The pattern is symmetric above and below the centre.
5
Measure b (half-width of central maxima): Using the millimetre scale on the screen (or a ruler), measure the distance from the exact centre of the bright central band to the centre of the first dark band on either side. This distance is called b. Take 2–3 measurements and average them for accuracy.
6
Record and calculate: Write D = 1000 mm and your measured b in the observation table. Calculate d = Dλ/b using λ = 6328 Å = 6.328 × 10⁻⁴ mm. This gives you d_calc for reading 1.
7
Change D and repeat: Move the screen to D = 1100 mm. Observe that the pattern has spread slightly — b is now a little larger. Measure the new b, record it, and calculate d again. Repeat for D = 1200, 1300, 1400 mm. You now have 5 readings for Wire 1.
8
Calculate mean d for Wire 1: Add up all 5 values of d_calc and divide by 5. This is your best estimate of Wire 1's thickness: d̄ = (d₁ + d₂ + d₃ + d₄ + d₅) / 5
9
Repeat for all 5 wires: Remove Wire 1 and mount Wire 2. Repeat steps 3–8 for each wire. Notice: thicker wires produce narrower patterns (smaller b), thinner wires produce wider patterns (larger b).
10
Plot the graph: For each wire, plot b (y-axis) vs D (x-axis). You should get a straight line. The slope of this line = λ/d. From slope, d = λ/slope. This is an independent verification of your result.

💻 How to Use This Simulation

i
Select a Laser from the top-left panel (He-Ne is default, λ = 632.8 nm). The laser beam colour on the canvas will change accordingly.
ii
Select a Wire (W1 to W5, thinnest to thickest). The wire thickness is shown below each button.
iii
Set D using the slider (700 to 1500 mm). Watch the diffraction pattern on the screen EXPAND as you increase D — this is exactly what happens in a real lab.
iv
Turn ON the Laser by clicking the red button. The animation starts, the beam glows, and the diffraction pattern appears on screen with b marked by arrows.
v
Add a Reading by clicking [＋ Add Reading]. The current D and b (with small realistic noise added) are recorded in the observation table on the right. The d_calc column shows "—" until you calculate.
vi
Take 5 readings by changing D to 700, 900, 1100, 1300, 1500 mm and clicking Add Reading each time. Each reading gives a slightly different b (due to noise), hence a slightly different d_calc.
vii
Click [▶ Calculate Mean d] — all d_calc values fill in instantly, and the mean d with standard deviation σ appears at the bottom of each wire's table.
viii
Switch wires and repeat. Or use [📋 Load Demo Readings] to instantly fill all 5 wires with sample data and then calculate.
ix
Go to Graph tab → click Refresh Graph → see the b vs D straight lines for each wire and the slope-based d calculation.

📋 What to Write in Your Lab Record

Aim: To determine the thickness of a thin wire using He-Ne laser diffraction.

Formula: d = Dλ/b, where D = wire-to-screen distance, λ = wavelength of laser, b = half-width of central maxima.

Observation Table: For each wire: Sr. No. | D (mm) | b (mm) | d = Dλ/b (mm) | Mean d (mm)

Result: The mean thickness of Wire 1 = ___ mm, Wire 2 = ___ mm, and so on.

Precautions: (1) Never look into the laser beam. (2) Keep room dark. (3) Measure b from exact centre of bright fringe to first dark fringe. (4) Do not disturb the laser or wire position during readings. (5) Use mean of multiple readings to reduce error.

GRAPH — b (mm) vs D (mm)

b=(λ/d)·D → straight line, slope=λ/d → d=λ/slope

Add readings in Simulation tab, then refresh.

QUIZ