Ray Optics and Optical Instruments

Introduction to Ray Optics and Optical Instruments

• Ray optics studies reflection, refraction, and dispersion of light with the ray picture of light
• Optical instruments discussed: plane/spherical surfaces, mirrors/lenses, and the human eye
• Light is electromagnetic radiation with wavelengths around 400 nm to 750 nm
• Light travels with immense speed (c ≈ 3×10^8 m/s in vacuum), highest speed attainable in nature
• Light travels in a straight line, however, light is also an electromagnetic wave
• Wavelength of light is tiny compared to ordinary objects, so it appears to travel in straight lines
• Path of light is called a ray, bundle of rays is a beam

Reflection of Light by Spherical Mirrors

• Laws of reflection state the angle of incidence equals the angle of reflection
• Reflected ray, incident ray and normal lie in the same plane
• Laws are valid for any reflecting surface, but discussion limited to spherical surfaces for simplicity
• Normal is along the radius, connecting center of curvature to point of incidence

Sign Convention

• Distances measured from the pole/optical center
• Incident light direction: distances are positive, opposite direction: negative
• Heights above the principal axis (x-axis) are positive, downwards are negative
• Accepted convention enables single formulas for spherical mirrors and lenses

Focal Length of Spherical Mirrors

• Parallel light beam converges to principal focus (F) on principal axis for concave mirror
• For convex mirror: Reflected rays appear to diverge from F on the principal axis
• If the parallel beam makes an angle with the principal axis, rays converge/diverge from a point in the focal plane (normal to the principal axis)
• Distance between focus F and pole P is focal length (f), where f = R/2 (R is radius of curvature)

The Mirror Equation

• The image is real where rays converge, virtual where they appear to diverge
• The image is a point-to-point correspondence with the object
• To locate an image, trace any two rays from a point on the object after reflection
• Four types of rays exist and can be traced

Mirror and Magnification Equations

• The mirror equation relates object distance (u), image distance (v), and focal length (f): (1/v) + (1/u) = (1/f)
• Linear magnification (m) is the ratio of the height of image (h') to height of the object (h): m = h'/h
• Sign convention for h and h': m = -v/u
• Equations are valid for all spherical mirrors and real/virtual images with proper sign convention
• The diagrams illustrate virtual image formation in either a concave lens or a convex mirror

Refraction

• Transparency allows some light to be reflected, while the rest enters a new medium
• A ray represents a light beam that travels in a transparent medium by refraction
• Refraction is the change in direction of light as it passes obliquely(0°< i < 90°) into another medium
• Snell experimentally derived that the Incident/refracted ray, and normal lie in the same plane
• The ratio of sines of incidence and refraction angles is constant (Snell's Law): sini/sinr = n21
• "n21" is the refractive index of medium 2 with respect to medium 1
• "n21 > 1": refracted ray bends towards normal, medium 2 is an optically denser
• "n21 < 1": refracted ray bends away, medium 2 is optically rarer

Refractive Index

• The formula explains refractive index relations
• The formula is n12 = 1/n21
• The second formula n32 = n31 x n12, for three media
• Rectangular slab: emergent ray is parallel to incident ray, but laterally shifted
• Water tanks appear shallower due to refraction, apparent depth (ha) = real depth (h2) / refractive index of water

Total Internal Reflection

• Light reflects back into same medium due to internal reflection
• Internal reflection occurs when light goes from a denser to a rarer medium
• Angle of refraction (r) is larger than angle of incidence (i); incident ray is partially reflected & transmitted
• The angle of incidence (i) increases, so does the angle of refraction (r)
• Ray bends further from normal until angle of refraction is π/2 = AO3D
• If incidence angle increases past critical angle: refraction is not possible > total internal reflection
• All incident light reflects for total internal reflection
• Incidence angle for angle of refraction at 90° is critical angle (ic): sin ic = 1/n

Refraction and Technilogical Applications including Total Internal Reflection

• Prisms bend light by 90° or 180° using total internal reflection and the material must have less than 45° critical angle
• Audio and video signals travel long distances in optical fibers because of total internal reflection use with composite glass/quartz
• A signal directed into can undergo many total internal reflections and emerge, with out losing signal

Spherical Surfaces and Lenses

• Refraction at a singular interface is described
• An infinitesimal part of a spherical surface shows the equations for refraction at plane surfaces
• Perpendicularity like a spherical mirror demonstrates what shows the formulas we use
• A thin lens uses one/more of those surfaces and the image is formed by them
• The final equation is the equation for the lens makers' formula

Refraction at a Spherical Surface

• Shows the equations for a point object producing a spherical image on the principal axis using two mediums and center
• Assumes small aperture (the size of the lens is small)
• MN is equivalent is the perpendicular length from the point
• OM, IM, and CM show magnitudes

Equations for Refraction at a Spherical Surface

• Shows the equation for the exterior angles for refraction at a spherical surface I = ∠NOM + ∠NCM
• Now Snells law says the final equation needs to apply the cartesian coordinates to solve the equation
• N2/v - N1/u = N2 - N1 /R In terms of the medium and the radius of curvature it shows objects and images

Refraction by a Lens

• One diagram showing image for lens the lens is shown
• Another that that applies after that one
• The thin lens is the thing that comes after this where BI1 = DI1 and N->infinity

Power of a Lens

• Describes that light converges when light passes through a material of lens
• Focal length is the power of a lens and the equations that that applies
• SI units for a lens use dioptre's
• Describes the equations and the example for this

Problems for a lens with Equations

• Explores combination of the lens with focal length and placed together to make a material
• Talks about lenses when close to each other
• Discusses what happens to the images in certain conditions

Optical Instruments and Ray Diagrams

• Optical Instruments that have been discovered and what they have achieved to learn from
• Focuses light and can have it magnify
• Discusses the distance light is at and how you can adjust what is right in front you

The Telescope

• The uses of a telescope
• What can occur because of the telescope
• Light and objects that we can find and look into in the galaxy and world