Light & Lenses — Image Cases Complete Study Guide

Document Specifications and Worksheets

• Specific printing instructions mandate: Print at 100% / Actual Size to preserve visual proportions and ray diagram accuracy.
• The content is split across two main parts: Light & Lenses — Image Cases (Part 1/2) and Light & Lenses — Image Cases (Part 2/2).
• Each page includes a designated My Notes header.
• Workspace prompts direct the reader to: Write rules / ray diagrams / examples here.

Fundamental Rules for Thin Lenses

• Thin Lens Equation: Relates focal length $f$, object distance $u$, and image distance $v$:   $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
• Magnification Equation: Relates magnification $m$, image height $h_i$, object height $h_o$, image distance $v$, and object distance $u$:   $m = \frac{h_i}{h_o} = \frac{v}{u}$
• Principal Ray 1 (Parallel Ray): An incident ray parallel to the principal axis refracts through the principal focal point $F_2$ of a convex lens, or appears to diverge from focal point $F_1$ of a concave lens.
• Principal Ray 2 (Focal Ray): An incident ray passing through (or directed toward) focal point $F_1$ refracts parallel to the principal axis.
• Principal Ray 3 (Central Ray): An incident ray passing through the optical center $O$ continues in a straight line without deflection.

Ray Diagrams and Image Cases for Convex Lenses (Part 1/2)

• Case 1: Object Positioned at Infinity ($u = \infty$)
  • Image Position: Formed at principal focus $F_2$.
  • Image Nature: Real and inverted.
  • Image Size: Point-sized / highly diminished ($m \ll 1$).
• Case 2: Object Positioned Beyond $2F_1$ ($u > 2f$)
  • Image Position: Formed between $F_2$ and $2F_2$.
  • Image Nature: Real and inverted.
  • Image Size: Diminished ($m < 1$).
• Case 3: Object Positioned at $2F_1$ ($u = 2f$)
  • Image Position: Formed at $2F_2$.
  • Image Nature: Real and inverted.
  • Image Size: Same size as object ($m = -1$).
• Case 4: Object Positioned Between $F_1$ and $2F_1$ ($f < u < 2f$)
  • Image Position: Formed beyond $2F_2$.
  • Image Nature: Real and inverted.
  • Image Size: Magnified ($m > 1$).
• Case 5: Object Positioned at Focus $F_1$ ($u = f$)
  • Image Position: Formed at infinity ($v = \infty$).
  • Image Nature: Real and inverted.
  • Image Size: Highly magnified ($m \rightarrow \infty$).
• Case 6: Object Positioned Between Optical Center $O$ and Focus $F_1$ ($u < f$)
  • Image Position: Formed on the same side of the lens as the object.
  • Image Nature: Virtual and erect.
  • Image Size: Magnified ($m > 1$).

Ray Diagrams and Image Cases for Concave Lenses (Part 2/2)

• Case 1: Object Positioned at Infinity ($u = \infty$)
  • Image Position: Formed at principal focus $F_1$ on the same side as the object.
  • Image Nature: Virtual and erect.
  • Image Size: Point-sized / highly diminished ($m \ll 1$).
• Case 2: Object Positioned Between Infinity and Optical Center $O$ ($\infty > u > 0$)
  • Image Position: Formed between optical center $O$ and principal focus $F_1$.
  • Image Nature: Virtual and erect.
  • Image Size: Diminished ($m < 1$).

Practical Applications and Examples

• Convex Lens Examples:
  • Magnifying Glasses: Uses Case 6 ($u < f$) to generate a virtual, erect, and magnified image.
  • Cameras: Uses Case 2 ($u > 2f$) to project a real, inverted, diminished image onto film or a sensor.
  • Projectors: Uses Case 4 ($f < u < 2f$) to produce an enlarged real image on a screen.
• Concave Lens Examples:
  • Correction of Myopia (Nearsightedness): Diverges parallel light rays entering the eye so the image focuses properly on the retina.
  • Peepholes (Door Viewers): Uses concave lenses to create a diminished, erect virtual image providing a wide view.