General Physics / Physics Dentistry - Light Reflection, Refraction, Optical Lenses

GENERAL PHYSICS / PHYSICS DENTISTRY

Course Codes: PHY111 / PHY181

Chapter 7: Light Reflection, Refraction, Optical Lenses and Image Formation

Definition and Properties of Light

• What is Light?

  • Electromagnetic radiation with wave properties.

  • Defined as photons that travel in collective rays in straight lines.

  • Divided into bands on the electromagnetic spectrum based on wavelength.

• Speed of Light:

  • Fastest material in the universe.

  • Measured in optical years: the distance light travels in one year.

  • Speed of light is approximately 300,000 kilometers per second (or 3 imes 10^8 m/s).

  • Light travels 18 million kilometers in one minute.

  • Time taken for light to travel from the Sun to Earth (approximately 150 million kilometers) is slightly over 8 minutes.

  • Daily travel distance: 25,925,000,000 kilometers; yearly travel: 9.46 imes 10^{12} kilometers.

The Ray Model of Light

• Light typically travels in straight lines.

• Represented using rays that are straight lines emanating from an object.

• This is an idealization that is beneficial for understanding geometric optics.

Reflection and Image Formation by a Plane Mirror

Law of Reflection

• The angle of reflection equals the angle of incidence, as measured from the normal to the surface.

Behavior of Light Ray on Encountering a Surface

When a light ray meets a surface, one of the following occurs:

1. Reflects off the surface at a different angle.

2. Passes into another medium, continuing on a straight path.

3. Is absorbed by the surface.

Types of Reflection

• Specular Reflection:

  • Light reflects at distinct angles which maintain the law of reflection.

• Diffuse Reflection:

  • Occurs when light reflects off a rough surface; angle of incidence varies.

• Visual Perception:

  • In diffuse reflection, the eye sees reflected light from many angles. In specular reflection, correct positioning is required to view the reflection.

Refraction

Definition

• Refraction: The bending of light as it transitions between different media.

  1. Light entering denser media (e.g., from air to water) bends towards the normal.

  2. Light entering less dense media (e.g., from water to air) bends away from the normal.

Refractive Index

• Indicates how much light slows down in a medium.

  • Defined as the ratio of the speed of light in a vacuum to the speed of light in that medium.

  • Generally, as the density of the medium increases, its refractive index also increases. Some notable exceptions exist, such as water.

• Velocity Relationship:

  • Velocity of light in a medium is inversely proportional to the refractive index:
    v ext{ (medium)} = \frac{c}{n}

  • If the refractive index (n) increases, the velocity (v) decreases.

  • Light perpendicular to the boundary remains unchanged in its direction but experiences a change in velocity due to the medium's density change.

Snell's Law

• Describes the relationship between angles of incidence and refraction at a boundary:
  n1 \sin(\theta1) = n2 \sin(\theta2)

1. If light travels from a rarer medium (lower n) to a denser medium (higher n), it bends towards the normal.

2. Example:

   • Given air (n1 = 1.00), optical fiber (n2 = 1.44), and incidence angle \theta1 = 22°, you find \theta2 with Snell's Law.

   • Calculation illustrates the refraction:
     \sin(\theta_2) = \frac{1.00}{1.44} \sin(22°) = 0.260

   • Therefore, \theta_2 = \sin^{-1}(0.260) = 15°.

Total Internal Reflection

• Occurs when light attempts to move from a medium with a higher index of refraction to a lower one; sufficient incidence angles must be met.

• Critical Angle (qc):

  • The angle of incidence at which the angle of refraction equals 90°.

  • If incidence angle exceeds this, total internal reflection occurs.

Application: Fiber Optics

• Utilizes total internal reflection, ensuring light is retained within optical fibers even when they bend.

• Images can be formed using groups of small fibers, demonstrating versatility in optical systems.

Optical Lenses and Image Formation

General Description of Lenses

• A Thin Lens is made of glass or plastic, shaped to have refracting surfaces that are segments of a sphere or a plane.

• Lenses can be classified as converging or diverging.

Types of Lenses

• Converging Lens:

  • Shape: Double-convex

  • Focal Length: Positive (+f)

  • Focus: Real

• Diverging Lens:

  • Shape: Double-concave

  • Focal Length: Negative (-f)

  • Focus: Virtual

Focal Points in Lenses

• Each lens has two focal points based on light direction; one from the left, another from the right.

Thin Lenses and Ray Tracing

• Ray Tracing:

1. For Converging Lens: Parallel rays converge at the focal point on the other side of the lens.

2. For Diverging Lens: Parallel rays diverge; the intersection point of rays when traced back is the focal point.

General Law of Lenses

• Governed by the laws similar to mirrors.

• Key variables include:

  • Object Distance (p)

  • Image Distance (q)

  • Focal Length (f)

  • Magnification (M)
    M = \frac{y'}{y} = -\frac{q}{p}

  • Positive M indicates an upright image; negative M indicates an inverted image.

Example Problems

• Example 1: Magnifying glass calculations involving object distance and focal length resulting in a virtual, upright, larger image.

• Example 2: Finding magnification of a diverging lens with specified object distance.

• Example 3: Deriving an expression for calculating magnification.

• Example 4: Problems involving the placement of objects creating various image types (real vs. virtual, enlarged vs. diminished).

Summary of Lenses

• Converging Lens: Thicker in the center; converges light to form a real focus.

• Diverging Lens: Thinner in the center and diverges light appearing to originate from a virtual focal point in front of the lens.

Sign Conventions:

• Distance (p and q) and height (y’) conventions are similar to mirrors.

• Ensure to be consistent when substituting signs during calculations.