Physics Notes on Convex and Concave Lenses

3.1 Convex Lens and Concave Lens

3.1.1 Classification of Lens

• There are two primary types of lenses:
    - Convex lens:
      - Thicker in the middle when compared to the edges.
    - Concave lens:
      - Thinner in the middle when compared to the edges.
• Applications of Convex Lens:
    1. Glasses for long-sightedness.
    2. Magnifying glass.
• Applications of Concave Lens:
    1. Glasses for short-sightedness.
    2. Peepholes in doors.

3.1.2 Converging Lens and Diverging Lens

• Convex Lens:
    - A convex lens converges light rays, hence is also called a converging lens.
• Concave Lens:
    - A concave lens diverges light rays, hence is also called a diverging lens.

3.1.3 Terminology

• Key Features of a Lens:
    - Optical centre (C): The central point of the lens.
    - Principal axis: A straight line drawn through the optical centre and perpendicular to the lens.
    - Principal focus (F):
      - For a convex lens, this is the point to which rays parallel to the principal axis converge after passing through the lens.
      - For a concave lens, this is the point from which rays appear to diverge after passing through the lens.
    - Focal length (f): The distance from the optical centre to the principal focus.
    - Focal plane: A plane that intersects the principal focus and is perpendicular to the principal axis.

3.2 Images Formed by a Convex Lens

3.2.1 Real Image and Virtual Image

• Real Image:
    - Light rays actually pass through a real image, which can be captured on a screen.
• Virtual Image:
    - No light rays actually pass through a virtual image, so it cannot be captured on a screen.

3.2.2 Construction Rules of Convex Lens

1. A light ray passing through the optical centre (C) travels straight on.
2. A light ray parallel to the principal axis passes through the principal focus (F) upon leaving the lens.
3. A light ray passing through the principal focus (F) becomes parallel to the principal axis upon leaving the lens.

3.2.3 Nature of Image at Different Object Distances

1. Objects between F and the lens:
      - Position of image: Beyond the object (same side as the object).
      - Nature of image: Virtual, erect, magnified.
2. Objects on F:
      - No image is formed (image at infinity).
3. Objects between F and 2F:
      - Position of image: Beyond 2F.
      - Nature of image: Real, inverted, magnified.
4. Objects on 2F:
      - Position of image: On 2F.
      - Nature of image: Real, inverted, same size as the object.
5. Objects beyond 2F:
      - Position of image: Between F and 2F.
      - Nature of image: Real, inverted, diminished.
6. Distant Objects (Objects at infinity):
      - Position of image: On the focal plane.
      - Nature of image: Real, inverted, diminished.

Summary of Object Position and Properties of Image

3.3 Magnification

Magnification Formulas

• There are two formulas for finding magnification (m):
    1. $m = \frac{h_i}{h_o}$
    2. $m = \frac{v}{u}$

Magnification Examples

Example 1:

• Given that the height of the object is 16 cm and the image height is 32 cm:
    - $m = \frac{32}{16} = 2$
• The image is magnified by a factor of 2.

Example 2:

• Given object distance (u) = 24 cm and image distance (v) = 18 cm:
    - $m = \frac{18}{24} = 0.75$
    - If the height of the object is 16 cm:
    - $h_i = 0.75 imes 16 ext{ cm} = 12 ext{ cm}$

Relationship between Magnification and Properties of Image

Advanced Ray Diagrams

1. Rule 4: (Head→Head, Tail→Tail): All rays from a point on an object that are refracted by the convex lens converge to, or appear to come from, the image of that point.
      - Example: Determine object distance (u) and image distance (v) for an object placed at 30 cm in front of a convex lens with a focal length of 10 cm:
      - $u = 30 ext{ cm}, ext{ } v = 15 ext{ cm}$
      - Nature of image: Real, inverted, and diminished.

2. Sketching Ray Diagrams:
      1. Mark F on the diagram.
      2. Draw light rays from the object.
      3. Determine the focal length based on the ray diagram.

3. Example with virtual image I formed by an object O:
      - Complete construction of rays showing virtual and real images through the lens.

Experimentation and Practical Applications

• Methods to find focal length using distant objects and plane mirror method.
• Observations from different angles can affect the perceived image through a convex lens.