Newton’s Rings: Lens Curvature R

Reflected Newton rings, air film, π phase jump. Measure dark-ring radii r_m and recover the hidden lens radius from a fit of r_m² versus m.

University / research· 24 min·Related simulator: Optics & LightNewton’s Rings

Goal

Determine R from r_m² = m λ R (contact, n = 1, dark centre). The slope of r² versus m is λ R, so R = slope / λ.

Equipment

Plano-convex lens on flat glass
Na-green source (known λ)
Travelling microscope

Experiment

Microscope: reflected Newton rings. No live radius on the bench.

Known λ = 550 nm. Air film (n = 1), optical contact, π phase jump on reflection is on. Lens curvature is unknown. Select dark-ring order m; the microscope reading appears only after you record.

Dark-ring order mm = 1

Microscope: no reading

Record m = 1… at least 6, then fit r_m² versus m.

Measurements

№	Order m	r_m µm	r_m² µm²
No measurements yet — take your first reading.

Data processing

Add at least 2 measurements to compute the fit.

Uncertainty

Lab report

Opens the system print dialog — choose “Save as PDF” or your printer. Header and footer are hidden when printing.

One click opens the print dialog — choose “Save as PDF”.

Newton’s Rings: Lens Curvature R

Generated: 24 Aug 2026, 22:31

Goal

Determine R from r_m² = m λ R (contact, n = 1, dark centre). The slope of r² versus m is λ R, so R = slope / λ.

Measurement table

#	Order m	r_m (µm)	r_m² (µm²)
No measurements yet — take your first reading.

Fit and derived value

Add at least 2 measurements to compute the fit.

Conclusion

The fitted curvature agrees with the hidden R. Main uncertainties: microscope noise, the paraxial gap t ≈ r²/(2R), and assuming a perfect contact (d₀ = 0).

PhysSandbox virtual lab — values come from your session; add your own discussion of error sources.

Theory

A spherical surface on a flat glass leaves an air gap t ≈ r²/(2R). With a π phase jump on one reflection, dark rings satisfy 2t = m λ, hence r_m² = m λ R. The bench hides R and never prints the first-ring radius.

Procedure

λ is known (550 nm). The lens radius R is hidden. Contact, air, phase jump are on.
Select ring order m and record the travelling-microscope radius r_m (µm). Small readout noise is added.
The notebook computes r². Repeat for m = 1… at least 6.
Fit r² (µm²) versus m; R = slope / (λ · 10¹²) in metres. Compare with the reference.

Conclusion

The fitted curvature agrees with the hidden R. Main uncertainties: microscope noise, the paraxial gap t ≈ r²/(2R), and assuming a perfect contact (d₀ = 0).