Notes on Chapter 23: Light - Geometric Optics

Chapter 23: Light: Geometric Optics

23.1 The Ray Model of Light

  • Ray Model of Light: Light often travels in straight lines; represented by rays that emanate from objects.

  • Utility: Simplifies analysis in geometric optics, particularly in explaining reflection and refraction.

23.2 Reflection; Image Formed by a Plane Mirror

  • Light Interaction with Surfaces:

    • Reflection: Some light is reflected; rest can be absorbed or transmitted.

    • Law of Reflection: The angle of reflection () equals the angle of incidence () with respect to the normal.

    • Types of Reflection:

    • Specular Reflection: Reflects in a uniform direction (e.g., from a mirror).

    • Diffuse Reflection: Reflects in many directions (e.g., from rough surfaces).

  • Images in Plane Mirrors:

    • The image appears behind the mirror.

    • Image distance equals object distance; height of image equals height of object (lateral magnification, m = 1).

23.3 Formation of Images by Spherical Mirrors

  • Types of Spherical Mirrors:

    • Concave: Reflective on the inside.

    • Convex: Reflective on the outside.

  • Parallel Rays: Incident parallel rays are not all focused at one point due to spherical aberration, which is mitigated using parabolic reflectors.

  • Focal Length:

    • Relation: f = \frac{R}{2} where R is the radius of curvature.

  • Ray Diagrams for Concave Mirrors:

    • Key Rays:

    1. Parallel to the axis reflects through the focal point.

    2. Through the focal point reflects parallel to the axis.

    3. Perpendicular to the mirror reflects back on itself.

    • Image Properties:

    • Images can be real and inverted or virtual and upright depending on the object’s position relative to the focal point.

23.4 Index of Refraction

  • Definition: Ratio of the speed of light in a vacuum (c) to its speed in the medium (v).

    • n = \frac{c}{v}

  • Values: e.g., Vacuum (1.000), Water (1.33), Glass (1.46), Diamond (2.42).

23.5 Refraction: Snell’s Law

  • Refraction: Change in light direction when crossing media boundaries.

  • Snell's Law: Relation between angles of incidence and refraction, given by:
    n1 \sin(\theta1) = n2 \sin(\theta2)

23.6 Total Internal Reflection; Fiber Optics

  • Occurs when light attempts to move from a medium of higher to lower refractive index. Critical Angle:
    \sin(\thetac) = \frac{n2}{n1} where (n1 > n_2).

  • Applications: Total internal reflection is used in fiber optics and binoculars.

23.7 Thin Lenses; Ray Tracing

  • Lenses: Converging (thicker in the center) vs. diverging (thicker at the edges).

  • Ray Diagrams:

    • For converging lenses, parallel rays focus at a point; rays through focal point exit parallel.

    • For diverging lenses, the opposite occurs.

  • Lens Power:

    • P = \frac{1}{f} ext{ (in diopters, D)} where f is the focal length.

23.8 The Thin Lens Equation

  • Thin Lens Equation: Similar to mirror equation: \frac{1}{f} = \frac{1}{do} + \frac{1}{di}

    • Sign conventions differ: positive for converging, negative for diverging lenses.

  • Magnification Formula: m = -\frac{di}{do}

    • Positive m indicates an upright image, negative indicates an inverted image.

23.9 Combinations of Lenses

  • Image formed by the first lens serves as the object for the second lens; object distances may be negative.

23.10 Lensmaker’s Equation

  • Relates radii of curvature and index of refraction to the focal length of a lens.

Summary of Chapter 23

  • Light travels as rays; reflection obeys the angle of incidence equals angle of reflection.

  • Plane mirrors produce virtual images; spherical mirrors can produce both real and virtual images.

  • Refraction and total internal reflection are key to understanding optics; lenses manipulate light to form images.

  • Essential equations include those for mirrors, lenses, and magnification, which aid in calculating image properties.