Refraction at a spherical surface
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Relation between object and image distance.
n₂/v − n₁/u = (n₂−n₁)/RFor a single surface: n₂/v − n₁/u = (n₂ − n₁)/R. Basis for the lens maker's formula.
n₁ = 1, n₂ = 1.5, R = 10 cm, u = −30: v = 45 cm.
Signs: R positive if the centre is on the outgoing side.
In more detail
Refraction at a spherical surface relates object and image distances through the surface curvature and refractive indices. It is the basis for lens and eye models.
Real-world uses
- Lens designers use spherical surface refraction to calculate lens shapes.
- Eye models use this formula for the cornea.
- Lens designers use the refraction formula for a curved surface to predict where an image forms inside a glass object.
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Frequently asked questions
What determines the image?
The refractive indices on both sides and the radius of curvature.
Is it approximate?
It applies to paraxial rays near the axis.
Why is this formula important?
It is the building block for lenses, because a thin lens is two curved refracting surfaces considered together.
Related topics in Optics
Rainbow formation · Scattering of light · Mirage · Thin lens · Lens formula · Lens maker's formula