Refraction at a Flat Surface
Why a pool looks shallower than it is.
Lesson at a glanceShow the key points
- Snell's law: sin i / sin r = v₁/v₂ = μ₂/μ₁; μ = 1 for vacuum (and almost for air).
- Rays from an object under a flat surface, viewed nearly normally, seem to come from a point closer to the surface: a virtual image.
- Viewed from air: μ = real depth / apparent depth (18.5).
- The image shifts toward the observer by Δt = (1 − 1/μ)t (18.6).
A swimming pool always looks shallower than it really is, and a straw in a glass looks bent at the surface. Both are images made by refraction at a flat surface.
Snell’s law with refractive indices
When a ray crosses from medium 1 into medium 2, the angles obey
The image formed by a flat surface
An object O lies in medium 1 (index μ₁) below a flat surface; medium 2 (index μ₂) is above. A ray OP straight up crosses without bending. A ray OA striking the surface at a small angle i bends to angle r. Traced back, the two rays meet at I, a virtual image of O.
For small angles, sin ≈ tan, so sin i ≈ PA/PO and sin r ≈ PA/PI, and Snell’s law gives
Looking from air (μ₂ = 1) at an object in a medium of index μ:
The object seems raised toward the observer by
A glass block (μ = 1.5) 4.5 cm thick rests on a page. How far raised does the print appear, viewed from above?
The bottom of a pool appears 1.5 m deep when viewed from directly above. How deep is it really? (μ of water = 1.33.)
- 1sin i / sin r = v₁/v₂ = μ₂/μ₁.
- 2A flat surface forms a virtual image of an object below it.
- 3Viewed from air near the normal: μ = real depth / apparent depth.
- 4The image is raised by Δt = (1 − 1/μ)t.
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