Refraction and lenses

View a submerged straw through the water's surface from air at a slant. Light from the straw speeds up and bends as it leaves water for air. Your eye traces the final direction backward to a shifted apparent position. The straw itself stays straight.

Frequency f counts complete wave cycles passing a point each second. Wavelength λ is the distance between neighbouring matching parts of a wave. Monochromatic light has one frequency. In v = fλ, v is wave speed. When this light crosses a stationary boundary from air into water, f stays fixed while v and λ decrease. With f unchanged, a lower v means a shorter λ.

A ray travelling along the normal can enter a slower material without turning. The normal is perpendicular to the boundary. Its speed and wavelength may change, but its direction stays the same. Bending towards or away from the normal requires nonzero incidence in these boundary cases.

For an ideal thin converging lens, place a stamp inside the focal length. Outgoing rays spread apart; backward extensions meet on the stamp's side of the lens. The image is virtual, upright and magnified. The observer views the outgoing light from the other side.

Beyond F, an ideal converging lens gives a real, inverted image on the far side. Beyond 2F it is reduced; at 2F it is same-size; between F and 2F it is magnified. A distant scene beyond 2F forms a real, inverted, reduced image on a camera sensor. Projectors form real screen images; the eye forms a real image on its retina. At F, there is no finite image.

Refractive index is n = c/v: c is light's speed in vacuum and v its speed in the material. A higher n means a lower speed. For light going from higher to lower index, the critical angle is the incidence angle, measured from the normal, whose refracted ray runs along the boundary. Above it, total internal reflection occurs. A fibre's core has a higher index than its cladding, so suitable rays reflect inside the core and carry signals.

For an oblique air-to-glass ray, ordinary glass has a higher refractive index and a lower light speed than air. The transmitted ray therefore bends towards the normal. Here n = c/v uses vacuum light speed c and material light speed v. To compare entering materials, hold the incident medium and nonzero angle fixed: a higher entering index gives a ray closer to the normal. Index difference alone is not a general bending rule.

For an ideal thin converging lens, trace two rays from one object point: a parallel ray through the far focus and a central ray straight through. Inside F, outgoing rays spread apart. Extend them backward to the object's side. Their extensions locate the virtual image. A screen there cannot display that image because the actual outgoing rays do not converge there.