Ray Optics: Reflection and Refraction

• Ray optics, also known as geometrical optics, describes light propagation in terms of rays.
• Simplifies light's behavior by assuming it travels in straight lines.
• Diffraction effects are negligible in ray optics.
• Ray optics is applicable when light interacts with objects larger than its wavelength.

Reflection

• Occurs when light bounces off a surface.
• The law of reflection states that the angle of incidence equals the angle of reflection.
• Angles are measured with respect to the normal, an imaginary line perpendicular to the surface at the point of incidence.
• Specular reflection happens on smooth surfaces, resulting in a clear reflected image.
• Diffuse reflection occurs on rough surfaces, scattering light in many directions.

Refraction

• Bending of light as it passes from one medium to another.
• Bending occurs due to changes in the speed of light in different media.
• Snell's Law relates the angles of incidence and refraction to the indices of refraction of the two media: n1sinθ1 = n2sinθ2.
• n1 and n2 are the refractive indices of medium 1 and medium 2.
• θ1 and θ2 are the angles of incidence and refraction.
• The refractive index of a medium is the ratio of the speed of light in a vacuum to its speed in the medium.
• When light enters a denser medium (higher refractive index), it bends towards the normal.
• When light enters a rarer medium (lower refractive index), it bends away from the normal.
• Total internal reflection occurs when light travels from a denser to a rarer medium 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.

Lenses

• A transparent object with curved surfaces that refract light.
• Convex lenses are thicker in the middle and converge light rays.
• Concave lenses are thinner in the middle and diverge light rays.
• The focal length (f) of a lens is the distance from the lens to the point where parallel rays converge (convex) or appear to diverge from (concave).
• The lensmaker's equation relates the focal length of a lens to its refractive index and the radii of curvature of its surfaces: 1/f = (n-1)(1/R1 - 1/R2).
• R1 and R2 are the radii of curvature of the lens surfaces; sign conventions apply where R is positive if the surface is convex to the incoming light and negative if concave.
• The thin lens equation relates the object distance (u), image distance (v), and focal length (f): 1/f = 1/u + 1/v.
• Object distance (u) is the distance from the object to the lens.
• Image distance (v) is the distance from the image to the lens.
• Magnification (M) is the ratio of the image height to the object height: M = v/u.
• A positive magnification indicates an upright image.
• A negative magnification indicates an inverted image.

Optical Instruments

• The human eye uses a lens to focus light onto the retina.
• Corrective lenses (glasses or contacts) compensate for vision defects like nearsightedness (myopia) and farsightedness (hyperopia).
• A simple microscope uses a single convex lens to produce a magnified virtual image of a small object.
• The angular magnification of a simple microscope is approximately 1 + (D/f), where D is the least distance of distinct vision (typically 25 cm).
• A compound microscope uses two lenses (objective and eyepiece) to achieve higher magnification.
• The objective lens forms a real, magnified image, which is then further magnified by the eyepiece.
• The total magnification of a compound microscope is the product of the magnifications of the objective and eyepiece lenses.
• A telescope is used to view distant objects.
• Refracting telescopes use lenses to collect and focus light.
• Reflecting telescopes use mirrors to collect and focus light.
• Angular magnification of a telescope is the ratio of the angle subtended by the image at the eye to the angle subtended by the object at the unaided eye.
• For a simple two-lens telescope, the angular magnification is approximately fo/fe where fo and fe are the focal lengths of the objective and eyepiece respectively.

Prisms

• A transparent optical element with flat, polished surfaces that refract light.
• Prisms are used to disperse light into its constituent colors (spectrum) due to the wavelength dependence of the refractive index (dispersion).
• 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.
• The refractive index (n) of the prism material is related to the angle of minimum deviation (δm) and the angle of the prism (A) by: n = sin((A + δm)/2) / sin(A/2).
• Prisms can also be used for total internal reflection, as in binoculars and periscopes.

Optical Aberrations

• Optical aberrations are imperfections in the image formed by a lens or optical system.
• Spherical aberration occurs because spherical surfaces do not perfectly focus light rays to a single point.
• Chromatic aberration occurs because the refractive index of a lens material varies with wavelength, causing different colors of light to focus at different points.
• Aberrations can be reduced by using aspherical lenses, multiple lens elements, or by carefully choosing lens materials.