Optics and Lenses Quiz

Chapter 1 - Reflection and Mirrors (Geometrical)

• Objectives: Students should be able to explain and illustrate reflection, absorption, and refraction of light rays using diagrams. They should also be able to graphically illustrate light reflection from plane, convex, and concave mirrors. Students should define and illustrate real, virtual, erect, inverted, enlarged, and diminished images, plus use geometrical optics to draw images of objects at various distances from converging or diverging mirrors.

Geometrical Optics

• Light travels in straight lines
• When light hits a boundary between two mediums (e.g., air and water), it may reflect, refract, or be absorbed.

Reflection, Refraction, and Absorption

• Reflection: Light rays bounce off a surface
• Refraction: Light rays bend when passing from one medium to another
• Absorption: Light rays are absorbed by a surface and do not reappear

The Laws of Reflection

• The angle of incidence equals the angle of reflection
• The incident ray, reflected ray, and normal all lie in the same plane

The Plane Mirror

• A mirror is a highly polished surface reflecting light uniformly
• Images appear to be equi-distant behind the mirror, but left-right reversed.
• Object distance (p) = Image distance (q)

Real and Virtual

• Real images can be projected onto a screen
• Virtual images cannot be projected onto a screen

Image of a Point Object

• Image appears to be the same distance behind the mirror as the object is in front.

Image of an Extended Object

• The image is forward-backward, right-left reversed.

Terms for Spherical Mirrors

• Concave mirror: Curved inward, like a cave
• Convex mirror: Curved outward, like a dome
• Axis: An imaginary line passing through the center of the mirror
• Vertex: A point at the mirror's center where the axis intersects the mirror's surface.
• Center of curvature (C): The center of the imaginary sphere the mirror belongs to.
• Radius of curvature (R): The distance from the vertex to the center of curvature.
• Focal point (F): The point where parallel rays converge after reflection from a concave mirror, or appear to diverge from a convex mirror.
• Focal length (f): The distance from the vertex to the focal point (f = R/2)

The Focal Length of a Mirror

• Focal length is half the radius of curvature

The Focus of a Concave Mirror

• Parallel rays converge at the focal point.

The Focus of a Convex Mirror

• Parallel rays appear to diverge from the focal point.

Image Construction

• Ray 1: Parallel ray reflects through/appears to from focal point.
• Ray 2: Ray through focal point reflects parallel to the axis.
• Ray 3: Ray through center of curvature reflects back on itself.

Object at Focal Point

• No image is formed; reflected rays are parallel, and never cross.

Object Inside Focal Point

• Image is erect (same orientation as object), virtual, and enlarged.
• The image is located behind the mirror.

Convex Mirror Imaging

• All images are erect, virtual, and diminished. Images get larger as the object approaches.

Converging and Diverging Mirrors

• Converging mirrors (concave) cause parallel rays to converge.
• Diverging mirrors (convex) cause parallel rays to diverge.

Summary (Definitions)

• Object distance (p): The distance from a mirror to the object.
• Image distance (q): The distance from a mirror to the image.
• Real image: Can be projected onto a screen.
• Virtual image: Cannot be projected onto a screen.
• Converging/diverging mirrors: Refers to the reflection of parallel rays from a mirror's surface.

Image Construction Summary

• Ray 1: Parallel ray reflects through/appears to from focal point.
• Ray 2: Ray through focal point reflects parallel to the axis.
• Ray 3: Ray through center of curvature reflects back on itself.

Mirror Equation

• 1/p + 1/q = 1/f (where p = object distance, q = image distance, and f = focal length)

Sign Convention

• Object distance (p): Positive for real objects, negative for virtual
• Image distance (q): Positive for real images, negative for virtual
• Focal length (f): Positive for converging mirrors, negative for diverging.
• Radius of curvature (R): Positive for converging mirrors, negative for diverging.

Magnification of Images

• M = y'/y = -q/p (where y' = image height, y = object height)

Alternative Solutions

• Formulas for calculating object distance (p), image distance (q), and focal length (f)

Summary-Lensmaker's Equation

• 1/f = (n-1)(1/R₁ + 1/R₂) where f = focal length, n = index of refraction, R₁ and R₂ are the radii of curvature of the lens surfaces.

Types of Converging Lenses

• Double convex lens
• Plano-convex lens
• Converging meniscus lens

Types of Diverging Lenses

• Double concave lens
• Plano-concave lens
• Diverging meniscus lens

The Focal Length of Lenses

• Positive for converging lenses.
• Negative for diverging lenses.

The Principal Focus

• Light passes through a lens in either direction, so there are two focal points.

Terms for Image Construction

• Near focal point: Same side of the lens as incident light.
• Far focal point: Opposite side of the lens from incident light.

Ray 1 through the Lens

• A parallel ray passes through the far focus of a converging lens or appears to come from near focus of a diverging lens.

Ray 2 through the Lens

• A ray passing through the near focal point (or toward the far focas) of a converging lens is refracted parallel to the lens axis.
• In a diverging lens the ray will appear to be going toward the near focal point.

Ray 3 through the Lens

• A ray passing directly through the center of the lens will continue in a straight line.

Images Tracing Points

• Draw an arrow to represent the object and trace rays from the arrow tip. The image is where the rays cross.
• The image can be erect or inverted.
• Real image is always on the opposite side of the lens, virtual on the same side.
• Is the image enlarged, diminished, or same size.

Object Outside 2F

• Inverted
• Real
• Diminished
• Image is located between F and 2F

Object at 2F

• Inverted
• Real
• Same size
• Image is located at 2F on other side

Object Between 2F and F

• Inverted
• Real
• Enlarged
• Image is located beyond 2F

Object at Focal Length F

• No image formed
• Parallel rays

Object Inside F

• Erect
• Virtual
• Enlarged
• Image is located on near side of lens

Review of Image Formations (Object outside 2F Region)

• Virtual
• Erect
• Enlarged

Diverging Lens Imaging

• All images are virtual, erect, and diminished.
• Images get larger as object approaches

Analytical Approach to Imaging

• Lens Equation: 1/p + 1/q = 1/f

• Magnification: M = y'/y = -q/p

Same Sign Convention as For Mirrors

• Object distance (p): Positive for real objects, negative for virtual
• Image distance (q): Positive for real images, negative for virtual
• Focal length (f): Positive for converging lenses, negative for diverging
• Height of image (y'): Positive for upright (erect), negative for inverted.

Alternative Solutions (solving for p, q, f)

Summary

• Converging lens: Thickest in the middle, refracts parallel light to a real focus.
• Diverging lens: Thinnest in the middle, refracts parallel light to appear to come from a focal point in front.

Summary (Lensmaker's Equation)

• R1 and R2 radii are interchangeable.
• R1 and R2 positive for outward convex surface, negative for inward concave.
• Positive f = converging lens. Negative f = diverging lens.

Summary (Mathematical Approach)

• Lens Equation: 1/p + 1/q = 1/f
• Magnification: M = y'/y = -q/p

Summary (Sign Convention)

• Object distance (p): Positive for real objects, negative for virtual objects
• Image distance (q): Positive for real images, negative for virtual images
• Focal length (f) and radius of curvature (R) positive for converging lenses/mirrors and negative for diverging ones.

Fiber Optics

• Fiber optic lines: strands of glass or transparent fibers
• Used for long-distance transmission of light and digital info (e.g. telephone, cable TV, internet, medical imaging)
• Advantages over copper wire: less expensive, thinner, lighter, more flexible, less flammable.

Fiber Optics (cont.)

• Three main components of an optical fiber
  • Core (thin glass center where light travels)
  • Cladding (optical material, lower index of refraction, reflects light back into core)
  • Buffer Coating (plastic coating protects from damage)

Fiber Optics (continued)

• Two types of optical fibers
  • Single-mode fibers: transmit one signal per fiber
  • Multi-mode fibers: transmit multiple signals per fiber.

Inferior Mirage

• The heat from the road causes air above it to be hotter
• The cool air above the hot air has higher refractive index
• Rays of light are refracted more and more nearly horizontal as they move off the ground
• The "puddle" of apparent water isn't real, but an effect produced by refraction.

Rainbows

• Sunlight enters a water droplet and is refracted, this creates a spectrum of colors
• At the back surface of the droplet there is total internal reflection.
• Sunlight leaves the droplet, again refracting.
• Colors exit at slightly different angles.

Human Eye

• Fluid-filled object that focuses images onto the retina
• The cornea and lens refract light; lens flexibility adjusted by ciliary muscles to focus images onto retina.
• Retina contains rods and cones for intensity and frequency detection.

Additional examples of problems and how to solve using formulas.

Test your understanding of lens types and their properties with this quiz. Explore the characteristics that distinguish converging lenses from diverging lenses, and review key equations like the lensmaker's equation. Perfect for students studying optics in physics.