Bright Newton's ring radius

Enter a non-negative ring order, the wavelength in nanometres, and the plano-convex lens radius of curvature in metres. The calculator applies the thin-film phase-reversal condition, returns the radius in metres and millimetres, and also reports the ring diameter. It uses order zero for the first bright ring, making the convention explicit so laboratory calculations and measured ring labels can be compared consistently.

Choose the bright-ring order consistently

Newton's rings appear when light reflects from the two boundaries of the thin air film between a gently curved lens and a flat glass surface. For reflected light, one of those reflections introduces a half-cycle phase reversal. The contact point is therefore dark in the ideal arrangement, while bright rings occur between successive dark rings. This calculator labels the first bright ring as order zero and uses the factor m plus one half. Enter 0 for that innermost bright fringe, 1 for the next bright fringe, and so on. This convention matters because some laboratory notes describe the first visible bright ring as ring 1 while still using a formula whose algebraic index begins at zero. If your source numbers bright rings from one, subtract one before entering the order here. Confirm that you are measuring a bright reflected ring rather than a dark reflected ring or a transmitted ring, since those cases use different conditions. A consistent order definition prevents a systematic half-order error that cannot be corrected by changing units or rounding the final radius.

Enter wavelength and lens curvature in the stated units

Provide the wavelength in nanometres and the lens radius of curvature in metres. A typical monochromatic visible-light wavelength might be around several hundred nanometres, while a laboratory plano-convex lens may have a curvature radius from a fraction of a metre to several metres. The calculator converts the wavelength to metres before applying the formula, so the computed radius is dimensionally consistent. Use the vacuum wavelength unless your experiment specifically defines a wavelength in another medium. The standard equation here assumes an air film with refractive index approximately one, normal or near-normal incidence, a spherical lens surface, and a film thickness much smaller than the curvature radius. The lens radius is not the physical radius of the circular lens aperture; it is the radius of the sphere from which the curved optical surface is formed. It is commonly supplied by the lens manufacturer or determined independently with a spherometer. Positive finite inputs are required because a zero or negative wavelength or curvature radius has no physical meaning in this model.

Interpret the calculated radius and diameter

The calculation uses r_m squared equals open parenthesis m plus one half close parenthesis times wavelength times R, where r_m is the bright-ring radius, m is the zero-based bright order, and R is the lens radius of curvature. The returned radius is the distance from the contact centre to the selected bright fringe, not the distance across the complete ring. For comparison with microscope or camera measurements, the calculator also returns the diameter, which is twice the radius. Values are provided in both metres and millimetres without imposing display rounding, allowing downstream software to choose precision appropriate to the experiment. Real rings can differ from the ideal prediction because of dust, imperfect contact, non-spherical surfaces, oblique illumination, broadband light, or a liquid filling the gap. When estimating an unknown curvature radius or wavelength, measuring several rings and fitting radius squared against order is generally more robust than relying on a single fringe. This tool performs the forward ideal-model calculation and does not fit experimental observations or estimate uncertainty.