Ray Optics: Reflection and Refraction

• Ray optics (geometrical optics) describes light propagation via rays.
• Light rays travel in straight lines, with paths following reflection and refraction laws at media interfaces.
• It's an approximation for when light's wavelength is far smaller than encountered objects.
• Wave effects like diffraction and interference are not factored in with ray optics.

Reflection

• Reflection involves a wavefront's directional change at a media interface, redirecting it back into its original medium.
• Law of reflection dictates that the incidence angle equals the reflection angle.
• The incident ray, reflected ray, and the normal to the reflecting surface at the incidence point are coplanar.
• Specular reflection occurs on smooth surfaces and yields clear reflected images.
• Diffuse reflection scatters light in many directions, happening on rough surfaces.

Refraction

• Refraction is a wave's directional change as it moves from one medium to another, caused by speed variation.
• Refractive index (n) is the the ratio of light speed in a vacuum (c) to its speed in a medium (v), expressed as n = c/v.
• Snell's Law: n₁sinθ₁ = n₂sinθ₂, where n₁, n₂ are refractive indices, θ₁, θ₂ are incidence and refraction angles.
• The incident ray, refracted ray, and the normal to the refracting surface at the incidence point all lie in the same plane.
• Total internal reflection arises when light moves from higher to lower refractive index media.
• Incidence angle must exceed the critical angle (θc), where sinθc = n₂/n₁.
• Optical fibers and prisms utilize total internal reflection.

Lenses

• A lens is a transparent object that refracts light using curved surfaces, converging or diverging light rays.
• Converging (convex) lenses are thicker in the middle, focusing parallel light rays.
• Diverging (concave) lenses are thinner in the middle, spreading parallel light rays.
• Focal length (f) is the lens-to-focal point distance.
• Lensmaker's equation: 1/f = (n-1)(1/R₁ - 1/R₂), linking focal length to refractive index and surface curvature radii.
• Thin lens equation: 1/f = 1/do + 1/di (do = object distance, di = image distance).
• Magnification (M): M = hi/ho = -di/do (image height to object height ratio).
• Positive magnification indicates an upright image, while negative magnification indicates an inverted image.

Optical Instruments

• The human eye employs a lens to focus light on the retina.
• Cameras use lenses to focus light onto sensors or film.
• Magnifying glasses are converging lenses that produce enlarged, virtual images.
• Microscopes use objective and eyepiece lenses to generate highly magnified images of small objects.
• Telescopes utilize lenses or lens/mirror combinations to image distant objects.

Ray optics describes light as rays traveling in straight lines, governed by reflection and refraction laws. Reflection is the change in direction of a wavefront at an interface. The angle of incidence equals the angle of reflection, with all rays lying in the same plane.