Reflection and Refraction of Light

• Concave and convex mirrors, concave and convex lenses, and image formation can make the light chapter confusing.
• Solving numerical problems related to focal length, object distance, and image distance requires understanding and practicing image formation.
• Reflection, refraction, and refractive index are all covered
• Understand concepts and answer exam questions effectively.

Reflection of Light

• Reflection occurs when a light ray bounces back from a polished surface.
• Plane, concave, and convex mirrors exemplify polished surfaces.
• Reflection refers to the bouncing back of light from a polished surface like a mirror.

Laws of Reflection

• Angle of incidence equals angle of reflection (First Law).
  • Incident ray approaches the mirror.
  • Reflected ray moves away from the mirror post-reflection.
  • Normal is perpendicular to the mirror at the point of incidence.
  • Angle of incidence is between incident ray and normal.
  • Angle of reflection is between reflected ray and normal.
  • Angle of incidence = Angle of reflection in all types of reflection.
• Incident ray, reflected ray, and normal reside in the same plane (Second Law).
  • The plane is a flat surface.
• Laws of reflection are valid wherever reflection takes place.

Concave and Convex Mirrors

• Concave Mirror:
  • The inner, curved side is the reflecting surface.
  • Light striking the cave side indicates a concave mirror.
• Convex Mirror:
  • Light striking the opposite side of the cave indicates a convex mirror.
  • Both are spherical mirrors.

Terminology

• Pole:
  • The midpoint of the spherical mirror.
  • Denoted by P.
• Center of Curvature:
  • The center of the sphere from which the mirror is cut.
• Principal Axis:
  • The line joining the pole to the center of curvature.
• Radius of Curvature:
  • Distance from the pole to the center of curvature.
  • Mirror measurements are always from the pole.

Principal Focus (Focus)

• Parallel rays of light converge or appear to diverge from after reflection.
• Parallel rays of light must be used when referring to focus.
• Concave Mirror:
  • Parallel rays converge at a common point on the principal axis (focus).
  • Concave mirrors converge rays.
• Convex Mirror:
  • Parallel rays diverge.
  • Divergent rays extended backward meet at a common point on the principal axis (focus).
  • Convex mirrors diverge rays.

Focal Length

• Focal length is the distance from the pole to the focus denoted by 'f'.
• Focus (F) is the midpoint between the pole (P) and the center of curvature (C).
• Radius (R) is twice the focal length (f): R = 2f for both concave and convex mirrors.

Image Formation Basics

• At least two rays of light must meet from an object to form an image.
• Real Image:
  • Rays of light meet.
• Virtual Image:
  • Rays of light appear to meet.

Rules for Concave Mirror Image Formation

• Rule 1:
  • A ray of light parallel to the principal axis passes through the focus after reflection.
• Rule 2:
  • A ray of light passing through the focus becomes parallel to the principal axis after reflection.
• Rule 3:
  • A ray of light passing through the center of curvature retraces its path after reflection.
• Rule 4:
  • A ray of light incident at the pole reflects at the same angle, following the law of reflection.

Image Characteristics

• Consider image location relative to the mirror.

Different Cases of Concave Mirror

• Object Beyond C:
  • Image is between C and F.
  • Real, inverted, and diminished.
• Object at C:
  • Image is at C.
  • Real, inverted, and the same size.
  • Object and image are at the same location but inverted.
• Object Between C and F:
  • Image is beyond C.
  • Real, inverted, and magnified.
• Object at F:
  • Rays are parallel.
  • Image is at infinity.
  • Real, inverted, and highly magnified.
  • Parallel rays meet at infinity.
• Object Between F and P:
  • Real images are not formed
  • Image is behind the mirror.
  • Virtual, erect, and magnified.
  • Concave mirror produces a straight and enlarged image.

Summary

• As the object approaches, the image moves farther and becomes larger.
• Understanding all image formations is essential.
• Memorization is key.

Concave Mirror Uses

• Car Headlights and Torches:
  • The bulb is at the focus to produce parallel rays of light.
• Shaving Mirrors:
  • The object is between F and P, producing an upright and magnified image.
• Dentists:
  • Mirrors help see features in the mouth.
• Paper Burning:
  • Sunlight concentrates at the focus of the mirror, making it more intense.

Rules for Convex Mirror Image Formation

• Rule 1:
  • A ray parallel to the principal axis appears to diverge from the focus after reflection.
• Rule 2:
  • A ray of light directed towards the focus becomes parallel to the principal axis after reflection.
• Rule 3:
  • A ray of light appearing to go towards the center of curvature retraces its path.
• Rule 4:
  • A ray of light at the pole reflects at the same angle.

Image Cases

• Object at Infinity:
  • Image at the focus.
  • Image will be virtual, erect, point-sized.
• Object at Finite Distance:
  • Image will be between F and P, virtual, erect, and diminished.

Mirror Ussage

• Rear View Mirrors:
  • Provides an upright and wide field of view.
• Convex mirrors produce a virtual erect image.

Mirror Types and Characteristics

• The image quality is determined by its value.
• Concave Mirrors:
  • Form bigger, smaller, same size, inverted, and erect images.
• Convex Mirrors:
  • Always produce upright images.
  • Only upright, small images.

Sign Convention

• All distances are measured from the pole.
• Distances to the right (positive x-axis) are positive.
• Distances to the left (-x axis) are negative.
• Heights above are positive, and heights below are negative.

Mirror Formula

• 1/f = 1/v + 1/u
  • f = focal length
  • v = image distance
  • u = object distance
• U is always negative.
• Convex has a positive focal length.

Summary of Power and sign

• Concave power has a negative focal power.
• Always measure from the pole.
• The area above is the negative axis, meaning negative for everything.
• Mirror power is the image from the same position.

Manginification

• Magnification: Image quality
• H1/H0
• Minus v/u

Lenses

• Convex lens is similar to concave mirror.
• Opposites repel.

Lenses: Convex vs Concave

• Convex Lens:
  • Thicker in the middle.
  • Converging.
• Concave Lens:
  • Thinner in the middle.
  • Diverging.

Lenses

• Lens basics include optical center.
• Light passes through the optical center without deviation.
• Lenses always have two focal lights.
• F1 and F2 must be included.
• Optical is the one that is always used in the end

Primary Focus

• Similar to concave mirror.
• Convex lens focuses parallel lines.
• Concave lens makes parallel lines diverge.

Image fromation details

• Concave and convex lenses have two focal points.
• Lenses bend light based on whether they are coming from air or not.

Concave notes

• Convex copies the concave mirror.
• Always a real formation from a concave lens.
• Convex makes the inverted image on the other side.
• One straight line makes images.
• Straight image on the same side is always a thing.

Image keynotes for convace

• All the images run by the optical.
• The larger the size of the image, the closer it comes.
• Convace mirror images are smaller.

Rules

• Law 1: Pass all images through the focal point to converge on the other side.
• Law 2: Light from the center.
• Light passes through the center without deviation.

Formulas to note

• Power = 1/f
• If the same lenses are next to each other P = 1+2+3.
• F need to measure meter.
• Convex is positive.
• Convace is negative.

Key points

• Refraction:
  • Bending of light as it passes through, due to changes in speed.
  • Air to water example.
• From a rarer to a denser medium:
  • Light bends towards the medium.
• From a denser to a rarer medium:
  • Light bends away from the medium.

Refractive Index

• Indicates how dense the medium is.
• Water = speed is 5.
• Air = speed is 2.
• Air/water = refractive index.

Abosulute index

• If the first medium is air, the second can be anything; this is the absolute index.
• It is important to note if two mediums change.
• One and two and its reflection, the equal amount is key.

Important points for exam questions

• Angle of incidence and emergence are very similar.
• Both parallels angles

Snell law important points

• I1 x sin 1 = 2 x sin = constant numbers.