Geometrical optics

• Types of Reflection:

  • Regular reflection: smooth surfaces reflect rays of light in one direction only
  • Irregular reflection: rough surfaces reflect rays of light in many directions
• Spherical mirrors:

  • Concave Mirror:
  • Reflecting surface is the inner curved surface
  • Size of the image depends on the position of the object
  • Can form both virtual and real images
  • Convex Mirror:
  • Reflecting surface is the outer curved surface
  • Size of the image is always smaller than the object
  • Can only form virtual and erect images
  • Terminology:
  • Pole: midpoint of the curved surface
  • Centre of Curvature (C): centre of the sphere
  • Radius of Curvature (R): radius of the sphere
  • Principal Axis: line joining centre of curvature and pole
• • Principal Focus (F): point where rays parallel to the principal axis converge (real focus for concave mirror, virtual focus for convex mirror)
  • Focal length (f): distance from the pole to the principal focus measured along the principal axis
• • Occurs when a ray of light travelling in denser medium enters into a rarer medium and bends away from the normal
  • Critical angle is the angle of incidence that causes the refracted ray in the rarer medium to bend through 90
  • Beyond the critical angle, total internal reflection occurs
• Refraction of light:

  • Bending of light as it passes from one transparent medium into another
  • Laws of Refraction:
  • The incident ray, the refracted ray, and the normal at the point of incidence all lie in the same plane
  • Ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant (sin i / sin r = n, where n is the refractive index)
  • Refractive Index:
  • Ratio of the speed of light in air to the speed of light in the medium
  • Total Internal Reflection:
• Applications of Total Internal Reflection:

  • Totally Internal Reflecting Prism:
  • Used in optical instruments like cameras, binoculars, periscopes, and telescopes
  • Optical Fibre:
  • Used in telecommunication field for transmitting light over long distances with minimal energy loss
  • Light Pipe:
  • Bundle of optical fibres used to illuminate inaccessible places
  • Endoscope:
  • Medical instrument for exploratory diagnostics and surgical purposes, uses total internal reflection to transmit light
• Refraction through Prism:

  • Prism refracts light as it passes through, deviating the path of light
  • Emergent ray is not parallel to the incident ray, deviated by the prism
• Lenses:

  • Convex Lens:
  • Causes incident parallel rays to converge at a point
  • Thick at the centre and thin at the edges
  • Concave Lens:
  • Causes parallel rays of light to diverge from a point
  • Thin at the centre and thick at the edges
  • Terminology:
  • Principal Axis: line passing through the centres of curvatures
  • Optical Centre, C: point at the centre of the lens
  • Principal Focus, F: point where light rays travelling parallel to the principal axis converge for convex lens, appear to come from for concave lens
• • Focal Length, f: distance between the optical centre and the principal focus
  • Power of a Lens:
  • Defined as the reciprocal of its focal length in metres
  • Power of a lens = 1 / focal length in metres
  • SI unit is Dioptre (D), where 1 D = 1 m^-1
• Power of a lens is defined as "the reciprocal of its focal length in metres"
• 1 Dioptre (D) is the power of a lens whose focal length is 1 metre
• Focal length of a convex lens is positive, making its power positive
• Power of a concave lens is negative, as it has a negative focal length
• Image formation by lenses occurs through refraction, unlike mirrors which form images through reflection
• Convex lens image formation:

  • A ray parallel to the principal axis passes through the focal point after refraction
  • A ray passing through the optical centre passes straight through the lens
  • A ray passing through the focal point becomes parallel to the principal axis after refraction
• Lens formula:

  • 1/f = 1/p + 1/q
  • Sign conventions:
  • Focal length (f): positive for a converging lens, negative for a diverging lens
  • Object distance (p): positive for a real object on the left side of the lens, negative for a virtual object on the right side
  • Image distance (q): positive for a real image on the right side by a real object, negative for a virtual image on the left side by a real object
• Applications of lenses:

  • Camera:
  • A real, inverted, and diminished image is formed when the object is placed beyond 2F
  • Slide Projector:
  • Uses a converging or concave mirror and converging lenses to produce a real, large, and inverted image
  • Photograph Enlarger:
  • Uses a convex lens to produce a real, magnified, and inverted image
  • Object placed at a distance more than F but less than 2F
• Magnifying Power:

  • Given by M = 1 + (d/f)
  • A lens of shorter focal length has greater magnifying power
• Resolving Power:

  • Ability of an instrument to distinguish between closely placed objects or point sources
• Compound Microscope:

  • Consists of objective and eyepiece lenses
  • Provides greater magnification than a single lens
  • Magnification determined by L = (d/f) + 1
• Telescope:

  • Used to observe distant objects using lenses or mirrors
  • Refracting telescope uses two converging lenses
  • Magnification given by M = f/fo
• Human Eye:

  • Acts like a camera with a refracting system containing a converging lens
  • Accommodation:
  • Ciliary muscles control the curvature and focal length of the lens
  • Adjusts for objects at various distances
  • Near Point and Far Point:
  • Near point: minimum distance producing a sharp image on the retina
  • Far point: maximum distance on which the fully relaxed eye can focus
• Defects of Vision:

  • Nearsightedness (Myopia):
  • Inability to see distant objects clearly
  • Corrected with diverging lenses
  • Farsightedness (Hypermetropia):
  • Inability to form distinct images of nearby objects
  • Corrected with converging lenses
• Summary:

  • Power of a lens is the reciprocal of its focal length in metres
  • 1 Dioptre (D) is the power of a lens with a focal length of 1 metre
  • Refractive index is the ratio of the speed of light in air to the speed of light in a material
  • Refraction is the bending of light as it passes from one medium to another
  • Laws of refraction:
  • Incident ray, refracted ray, and normal lie in the same plane
• Critical angle is the angle of incidence for which the angle of refraction becomes 90 degrees
• When the angle of incidence is larger than the critical angle, total internal reflection of light occurs
• A simple microscope, also known as a magnifying glass, is a convex lens used to produce magnified images of small objects
• A compound microscope has two converging lenses: the objective and the eyepiece, and is used to investigate the structure of small objects
• Telescope is an optical instrument used to observe distant objects using lenses or mirrors
• A refracting telescope uses two converging lenses
• A reflecting power telescope replaces the objective lens with a concave mirror
• Magnifying power is defined as the ratio of the angle subtended by the image seen through the optical device to that subtended by the object at the unaided eye
• Resolving power of an instrument is its ability to distinguish between two closely placed objects
• Power of accommodation is the ability of the eye to change the focal length of its lens to form a clear image on its retina
• Nearsightedness is the disability of the eye to form distinct images of distant objects on its retina
• Nearsightedness can be corrected with glasses or contact lenses that use diverging lenses
• Farsightedness is the disability of the eye to form distinct images of nearby objects on its retina
• Farsightedness can be corrected with a suitable converging lens that refracts light rays more towards the principal axis before they enter the eye
• Reflection of light:

  • When light travelling in a certain medium falls on the surface of another medium, a part of it turns back in the same medium
• Laws of Reflection:

  • The incident ray, the normal, and the reflected ray at the point of incidence all lie in the same plane
  • The angle of incidence is equal to the angle of reflection (i = r)