Light: Reflection and Refraction

• Light enables sight and is associated with phenomena like image formation, twinkling stars, rainbows, and light bending.
• Light travels in straight lines, indicated by the sharp shadows cast by opaque objects.
• Diffraction occurs when light bends around small objects, challenging the straight-line assumption.
• The quantum theory of light reconciles the particle properties of light with the wave nature.
• Reflection and Refraction phenomena are studied by using the straight-line propagation of light.
• A highly polished surface like a mirror reflects most of the light.

Reflection of Light

• The angle of incidence equals the angle of reflection.
• The incident ray, the normal, and the reflected ray all lie in the same plane.
• Plane mirrors always form virtual and erect images.
• The image size is equal to the object size in a plane mirror.
• The image is as far behind the mirror as the object is in front, and is laterally inverted.
• Spherical mirrors are curved mirrors, commonly used type of curved mirror.

Spherical Mirrors

• A concave mirror curves inwards and faces towards the center of sphere.
• A convex mirror curves outwards.
• The pole (P) is the center of the reflecting surface of a spherical mirror.
• The radius of curvature (R) is the radius of the sphere of which the mirror is a part.
• The principal axis is a straight line through the pole and the center of curvature.

Concave Mirrors Ray Diagrams

• Caution: Looking directly at the Sun or its reflection can damage your eyes.
• The focus (F) of a concave mirror is where parallel rays converge.
• Sunlight is converged at a sharp, bright spot by the mirror, creating heat.
• The distance from the mirror to this spot approximates the focal length.

Convex Mirrors Ray Diagrams

• Rays parallel to the principal axis appear to diverge from a point (the principal focus) on the principal axis.
• principal focus is represented by the letter F.
• Focal length (f) is the distance between the pole and the principal focus.

Aperture

• The reflecting surface is spherical, having a circular outline.
• The diameter of the reflecting surface is the aperture (MN).
• Only mirrors with an aperture much smaller than their radius of curvature are considered.
• Focal Length of Spherical Mirrors: R = 2f, The principal focus lies midway between the pole and center of curvature
• Image formation depends on the object's position relative to the pole, focus, and center of curvature.
• Images can be real or virtual, enlarged, diminished, or the same size.

Activity 10.3

• Activity demonstrates finding focal length and observing image characteristics with a concave mirror.
• Activity should be done by determining focal length and observing image characteristics with a concave mirror.

Image Formation

• Nature, position, and size of the image by a concave mirror depends on the object position relative to P, F, and C.
• The image formed is real for some object positions, and virtual for others.
• The object position determines if the image is magnified, reduced, or the same size.

Ray Diagrams

• Ray diagrams can be used to study image formation by spherical mirrors.
• Each point on an extended object acts as a point source.
• Two rays from each point are typically used for clarity:
  • A ray parallel to the principal axis passes through the principal focus (concave) or appears to diverge from it (convex).
  • A ray passing through the principal focus emerges parallel to the principal axis.
  • A ray through the center of curvature returns along the same path.
  • A ray incident obliquely at the pole is reflected obliquely, with equal angles to the principal axis.

Concave Mirror Image Formation

• Ray diagrams illustrate image formation for various object positions.

Convex Mirror Image Formation

• Ray diagrams illustrate image formation for various object positions.

Concave Mirror Uses

• Concave mirrors are used in torches, searchlights, and vehicle headlights for parallel light beams.
• They are used as shaving mirrors for larger images of the face.
• Dentists use them for enlarged images of teeth.
• They are used to concentrate sunlight in solar furnaces.

Convex Mirror Image Formation

• Image formation is for convex mirrors.

Convex Mirror Activity

• An activity using a convex mirror, is used to determine image formation.

Convex Mirrors Image Formation Ray Diagrams

• Summarized in a table.

Full Image Comparison

• An activity that compares plane, concave, and convex mirrors for full image.

Convex Mirror Uses

• Convex mirrors provide an erect, diminished image and a wider field of view
• This helps see traffic in rear-view mirrors of vehicles.

Sign Convention

• The New Cartesian Sign Convention is used for reflection by spherical mirrors
  • The pole (P) is the origin.
  • The principal axis is the x-axis.
  • Object is placed to the left.
  • Distances to the right are positive.
  • Distances to the left are negative.
  • Distances above are positive.
  • Distances below are negative.

Mirrors: Formula and Magnification

• Object distance (u) is the distance of the object from the pole.
• Image distance (v) is the distance of the image from the pole.
• Focal length (f) is the distance of the principal focus from the pole. -Mirror Formula: 1/v + 1/u = 1/f
• Apply the New Cartesian Sign Convention when solving problems.

Lens: Magnification

• Magnification (m) is the ratio of image height to object height. Formula: m = h'/h
• The magnification is also related to object and image distances: m = v/u
• A positive image height indicates a virtual image.
• A negative image height indicates a real image.

Example 10.1

• Using parameters and equations to find image position, nature, and size.

Example 10.2

• Using parameters and equations to find image position, nature, and size.

Refraction

• Refraction is the bending of light as it passes from one transparent medium to another.
• The bottom of a tank or Lemon in water appears raised.
• A pencil partly immersed in water appears displaced.
• The extent of displacement depends on the media involved.
• Light does not travel the same way in all mediums.

Refraction Law

• When travelling obliquely from one material to another, the direction of propagation of light changes.
• Various activities help understand phenomenon of refraction.

Activity 10.7

• Demonstrates light refraction using a coin at the bottom of a bucket of water.

Activity 10.8

• Demonstrates light refraction using coin in a shallow bowl.
• The coin appears raised above its actual position.

Activity 10.9

• Activity to see the effects of placing a glass slab in relation to a line.

Rectangular Glass Lab

• Demonstrates refraction of light through a glass slab.

Activity 10.10

• Pins placed through the glass and tracing the path.
• Light Ray Changes:
  • Incidence at O means from air to glass; the ray bends toward the normal.
  • At O, it is glass to air and the light bends away from the normal.
• The emergent ray is parallel to the incident ray but with slight shift sideward.
• Refraction is caused due to change in the speed of light when moving between different mediums.

Refraction Laws

• The incident ray, refracted ray, and normal all lie in the same plane.
• Snell's Law: sin i / sin r = constant
  • i is the angle of incidence.
  • r is the angle of refraction.
• The refractive index is a constant value.

Refractive Index

• The change in direction of light in two mediums is measured by refractive index.
• Refractive index links speed of propogation of light in different mediums.
• Light travels fastest in vaccum: 3 x 10^8 m/s.
• Speed is reduced in glass and water.
• The refractive index for media depends on speed of light in the two media.
• Refractive index of medium 2 with respect to medium 1: n21 = (speed of light in medium 1) / (speed of light in medium 2) = v1/v2
• Refractive index of medium 1 with respect to medium 2: n12 = (speed of light in medium 2) / (speed of light in medium 1) = v2/v1
• If medium 1 is a vaccum it's called "Absolute Refractive Index" and simply represented with n with subscript 2.
• n = (speed of light in air) / (speed of light in medium) = c/v

Example of Refractive Index for Materials

• The refractive index of water (n) is 1.33, so the speed of light in air and water is 1.33.
• Crown glass (n) is 1.52.
• Must be accurate with the data.

Optical Density

• The ability for a medium to refract light also is measured with optical density.
• Rarer medium is optically rarer medium and denser medium is optically denser medium in comparison.
• Medium of largest refractive inedx is optically denser than the one on the other side.

Lens

• Lenses: are curved thicker in the middle or edges.
• Convex lenses converge beams like watchmakers.
• Concave lenses diverge beams.
• Spherical lenses are transparent material for two surfaces and at least on spherical surface.
• A lens with two spherical surfaces bulging outwards is a double convex lens = convex lens.
• A convex lens is thicker in middle than at edges and converges light rays = converging lens.
• A Double concave les has two spherical surfaces curved inwards.
• A Double concave lens/Concave lens is thicker at edges than middle diverges light rays = diverging lenses.

Diagram

• diagrams helps show two spherical surfaces of lens form of sphere.
• center of curvature of lens is sphere which is called the two/each of spherical surfaces.
• an imaginary straight line running though both centers of curvature for lens is that is called the principal axis.
• lenses of center point where all the lights goes through lens = optical center.
• a ray of light running though center of lens runs without deviation.
• Lens Aperture: The area of the circle defining the boundary of a spherical lens
• lens aperture is lower that the radius both centers of curvature are = equidistant.

Parallel Rays

• thin-lenses with small apperatures shows what would happen to parallel rays.
• caution: do not use with the sun or would cause damage in eyes.

Experiment

• The experiment must show why the paper would burn and make smoke or fire with use of a convex lens with rays of sun.
• a sharp spot on the paper from lens is real image of sun and concentrates sunlight on point generation heat.
• consider what happens if put rays of light parallel to what would happen if run through a lens with the result it be illustrated in (Fig.10.12) (a) convex /concave lens in (b).
• focus with the convex will have light reach /several rays light/ parallel refracted and converge to one point = the principle focus.
• opposite for with concave with each the rays refracting and light diverging the point on axis that the light makes is the concave principal focus.
• if run parallel light through of opposite of lens there is another principle focus on opposite sides and the two are called F1 and F2, the distances are called the "Focal point" which is noted at "f."
• focal length = if use convex look at Activity 10.11, and move lens toward sun and distance from it that will provide the focal length.

Lens Images

• Lenses form images by refracting light and images can be analyzed to see nature.
• Experiment using convex lens to find its length and then 5 parallel lines in chalk on long where the 5 succesive lines show the focal parts for the lens.

Focus

• place convex lens on stand on line that's center focus for length over the lines, the use the lines on the side where is the 2F and make with Letters like 2F1, F1, F2, and 2F₂ respectively,
• Placing a burning candle at the far beyond side and have the sharpe clear image on the screen and then mark, the nature, size etc, The repeat but putting object behind 2f, 1 and between F and Tabulate the data for the nature with size by putting it down and writing down for the lens.

Table 10.4

• Nature, position and relative size of the image formed by convex.

Concave vs Convex

• Concave is a action.
• always small
• diminished with object.

Ray Diagram

• the lens is used with Ray diagrams to represent what happens with the image to help see nature/ size/ position.
• diagrams in lenses with (Fig12A/B) in lines and of spherical mirrors what considers with falling rays.
  • First ray on the object light that is parallel on axis after move through a convex / from a the focus (Fig1.13(1)
  • if concave its the lens makes it diverge and the to point principle focus on sides = 10.13(b)

Chart

• Chart for what happens with parallel/ what is with side (fig 14a)
• for concave Fig1.14b the light coming from the principle will be parallel.
• for third line from axis after center will not to side = the light comes through with deviation as it is illustration of Fig 10.15(a) or (b).
• The ray diagrams can work with both convex/concave can what with the various point along.

Lenses: Sign vs Nature/Position

• For lenses follows sign for mirrors where is sign of the distance that uses what to make what comes with the lens.
• with these sign with distance and follow from center use sign rules with values, the value will tell what sides need/ what you do and where on the lens.

Lenses: Nature vs Magnifcation

• For lenses we have that has magnification that what like in spherical mirrors for distances/ formula what how from to that will work.
• for distances for what to use with.
  • object distances (u). and image differences (v), lens focal point by (f).
  • Lenses in 1 or u with (10.8) where
  • 1 and (f)
• The that general used will valid situations how the side the values of what is for you need and use what is needed.