Newton's Ring experiment

Newton's Ring experiment

1. What It Is

Newton's rings = concentric circular interference fringes formed by division of amplitude in the air film between a plano-convex lens (radius $R$ large) and a flat glass plate, illuminated from above with monochromatic light.

Observed by reflected light (or transmitted) through a microscope.

2. Geometry and Path Difference

Air film thickness at distance $r$ from contact point $O$ (where lens touches plate):

derived from circle geometry $(R -t)² + r² = R² ⇒ t = R - √(R² - r²)≈ r²/(2R)$ for $r≪R$.

Light reflects from top of air film (glass→air, no flip) and bottom (air→glass, half-wave π flip). So for reflected system:

Constructive/destructive at eye:

• Dark (destructive) reflected:

• Bright reflected:

Since $t=r²/(2R)$:

for reflected light. Central spot ($t=0$) ⇒ $r=0 ⇒ dark in reflected; bright in transmitted (no half-wave difference).

3. Setup (diagram description)

Monochromatic source → 45° glass plate → plano-convex lens (R) on glass plate
                       ↓ reflected beams from top/bottom of air film interfere → microscope sees rings

White light gives coloured rings (few orders). Sodium light $λ=589$ nm gives clear.

4. Applications (what examiners ask)

• Measure $λ$: with known $R$, measure diameter $D_n =2r_n$ for $n$th dark ring:

. Use two rings to avoid contact error:

• Measure $R$ (lens curvature):

• Refractive index of liquid: fill air film with liquid $μ$: $r_n² = nλR/μ$ ⇒

5. Transmitted Rings (complement)

Without half-wave both reflections? Transmitted system: $Δ=2t$ (no extra $λ/2$) ⇒ bright/dark swapped vs reflected; transmitted rings fainter (less contrast) because intensities differ.

6. Worked Examples

(a) λ=600 nm, R=1.0 m, 10th dark ring: r =√(10·6e-7·1)=√6e-6≈2.45 mm, D≈4.9 mm ✓

(b) Diameters D5=3.0 mm, D15=5.1 mm, λ=589 nm ⇒ R=(D15²-D5²)/(4·10·λ)= (26.01-9)·10^{-6}/(2.356e-5)≈0.72 m ✓

(c) Why central dark? t=0 ⇒ Δ=λ/2 ⇒ destructive ⇒ dark (reflected) ✓

(d) Liquid μ? Air ring D=4 mm becomes 3.5 mm in liquid: μ=(4/3.5)²≈1.31 ✓

7. Exam Points

• Diagram + formation and path difference $Δ=2t+λ/2$ — 5 marks, almost certain.
• Derive $r_n=√(nλR)$ (dark reflected) — 7 marks, very frequent.
• Use $λ = (D_{n+m}²-D_n²)/(4mR)$ to find $λ$ or $R$ or $μ$ — 5-7 marks, very frequent.
• Explain central dark (reflected) vs bright (transmitted) — 3-5 marks, frequent.