Ray Optics: Reflection and Refraction

• Ray optics, also known as geometrical optics, describes light propagation in terms of rays.
• Rays travel in straight lines and their paths are governed by the laws of reflection and refraction at interfaces between different media.
• It is an approximation valid when the wavelength of light is much smaller than the size of the objects it encounters.

Reflection

• Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated.
• Specular reflection is reflection from a smooth surface, such as a mirror.
  • In specular reflection, the angle of incidence equals the angle of reflection.
  • The incident ray, the reflected ray, and the normal to the surface at the point of incidence all lie in the same plane.
• Diffuse reflection is reflection from a rough surface.
  • In diffuse reflection, light is scattered in many directions.
  • The law of reflection still holds locally at each point on the surface.

Refraction

• Refraction is the change in direction of a wavefront passing from one medium to another.
• Snell's Law describes the relationship between the angles of incidence and refraction, and the refractive indices of the two media.
  • n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively.
  • The refractive index of a medium is the ratio of the speed of light in a vacuum to the speed of light in the medium.
• The frequency of light remains constant during refraction, while the wavelength and speed change.
• When light passes from a medium with a lower refractive index to a medium with a higher refractive index, it bends towards the normal.
• When light passes from a medium with a higher refractive index to a medium with a lower refractive index, it bends away from the normal.
• Total internal reflection occurs when light traveling in a medium with a higher refractive index strikes an interface with a medium of lower refractive index at an angle of incidence greater than the critical angle.
  • The critical angle is the angle of incidence for which the angle of refraction is 90 degrees.
  • sin(θc) = n2 / n1, where θc is the critical angle, n1 is the refractive index of the medium where the light originates, and n2 is the refractive index of the other medium.

Lenses

• A lens is a transparent object with curved surfaces that refracts light to form an image.
• Convex lenses are thicker at the center and converge light rays.
• Concave lenses are thinner at the center and diverge light rays.
• The focal length (f) of a lens is the distance from the lens to the point where parallel light rays converge (for a convex lens) or appear to diverge from (for a concave lens).
• The lensmaker's equation relates the focal length of a lens to its refractive index, the radii of curvature of its surfaces, and the refractive index of the surrounding medium.
  • 1/f = (n-1) * (1/R1 - 1/R2), where n is the refractive index of the lens material, R1 is the radius of curvature of the first surface, and R2 is the radius of curvature of the second surface.
• The thin lens equation relates the object distance (u), the image distance (v), and the focal length (f) of a lens.
  • 1/f = 1/u + 1/v
• Magnification (M) is the ratio of the image height to the object height.
  • M = h'/h = -v/u, where h' is the image height, h is the object height.
  • A positive magnification indicates an upright image, while a negative magnification indicates an inverted image.
• Real images are formed when light rays actually converge at a point and can be projected onto a screen.
• Virtual images are formed when light rays appear to diverge from a point and cannot be projected onto a screen.

Optical Instruments

• The human eye is an optical instrument that uses a lens to focus light onto the retina.
• A camera uses a lens to focus light onto a sensor or film.
• A telescope uses lenses or mirrors to magnify distant objects.
  • Refracting telescopes use lenses.
  • Reflecting telescopes use mirrors.
• A microscope uses lenses to magnify small objects.
• Angular magnification is the ratio of the angle subtended by the image at the eye to the angle subtended by the object at the eye.
• For a simple magnifier, the angular magnification is approximately M = 1 + (D/f), where D is the least distance of distinct vision (typically 25 cm) and f is the focal length of the lens.

Prisms

• A prism is a transparent optical element with flat, polished surfaces that refract light.
• Prisms are used to disperse light into its constituent colors, reflect light, or invert images.
• The angle of deviation (δ) is the angle between the incident ray and the emergent ray.
• The angle of minimum deviation (δm) occurs when the angle of incidence equals the angle of emergence.
• For a prism with small angle A, the angle of deviation is approximately δ = (n-1)A, where n is the refractive index of the prism and A is the angle of the prism.
• Dispersion is the phenomenon in which the refractive index of a material varies with the wavelength of light.
• Prisms can be used in spectrometers to analyze the spectral composition of light.

Explores ray optics, detailing light propagation via rays and the laws governing reflection and refraction. Covers specular reflection (smooth surfaces, equal angles) and diffuse reflection (rough surfaces, scattered light). Describes how the law of reflection still holds locally.