Spherical Mirror Equation Calculator
Applies the paraxial spherical-mirror equation to image location. Changing an input shows how the reported quantity responds.
Set the optical distances
Mirror image distance
From sample inputs to mirror image distance
The starting condition is Focal length = 0.25 m; Object distance = 0.4 m. It gives a fixed reference result before any input is changed.
After solving for mirror image distance, rearrange di = 1 / (1/f − 1/do) for one entered quantity. Recovering that entry checks a different algebraic direction instead of repeating the same calculation.
Tracing the ray relationship
Applies the paraxial spherical-mirror equation to image location. The calculation keeps focal length, object distance visible and reports mirror image distance in m.
Use the focal-length and distance signs belonging to the chosen mirror convention, especially for convex mirrors and virtual images.
The spherical mirror equation page labels each value before it enters the equation. That prevents an angle convention, temperature scale, optical sign, or reference quantity from becoming an invisible assumption.
Following di = 1 / (1/f − 1/do)
For spherical mirror equation, identify mirror image distance as the sought quantity and copy the printed relationship before using the sample data. This establishes an auditable direction for the arithmetic.
Write the spherical mirror equation relationship symbolically, reduce its units, and only then evaluate the numbers.
Audit the angle and length units
Reduce the dimensions in di = 1 / (1/f − 1/do) until they agree with m. For logarithms, trigonometric functions, and ratios, also verify that their arguments are dimensionless and inside the permitted domain.
Change one source value slightly and predict the direction of mirror image distance first. If the screen moves the other way, revisit the equation, signs, and reference frame.
What Spherical Mirror Equation does not include
The spherical mirror equation relationship uses paraxial rays or an ideal interference geometry. Thick elements, aberrations, polarization, dispersion, and large angles may require a more complete optical model for mirror image distance.
Carry this boundary with mirror image distance whenever the spherical mirror equation result is compared with measurement.
Using mirror image distance beyond this page
The displayed decimals make spherical mirror equation reproducible but do not improve its source data. Round only after the last dependent step.
Record the operating condition, formula, units, and convention beside mirror image distance. Those details distinguish a physically reproducible answer from a number copied out of context.
Another useful step from Spherical Mirror Equation
From this result, compare optical magnification calculator, lens power calculator, thin lens image distance calculator and combined lens power calculator.
Before following a link, confirm that its idealizations agree with the Spherical Mirror Equation model.
What to know about Spherical Mirror Equation
What does mirror image distance represent?
It is the value of di = 1 / (1/f − 1/do) under the units, field meanings, and optics assumptions printed on the spherical mirror equation page.
How can mirror image distance be checked?
Rearrange di = 1 / (1/f − 1/do) to recover an entered value, reduce the surviving unit to m, and compare the scale with the physical setup.
Do the displayed units matter?
Yes. Convert each measurement to the unit beside its field before evaluating the spherical mirror equation relationship.
Why might another mirror image distance differ?
Another medium, temperature, geometry, reference frame, boundary condition, or sign convention can change the reported mirror image distance.
Can mirror image distance be negative?
On the spherical mirror equation page, a negative value is meaningful only when the printed sign convention and equation permit it; otherwise it signals an invalid domain.
How should the result be rounded?
Keep guard digits while mirror image distance enters another operation, then report only the precision supported by the least certain source measurement.