Principles of Light Reflection and Refraction
Image Formation by Mirrors and Lenses
1. If reflected or refracted rays never meet, the image is virtual because the rays only appear to meet when extended backward. This occurs in plane and convex mirrors, in diverging lenses, or in converging lenses when the object is inside the focal point (F).
Refraction Fundamentals
2a. Refraction is the bending of light as it changes speed moving between media.
2b. Rules for Bending Light:
- (1) Low $\to$ high density = toward the normal.
- (2) High $\to$ low density = away from the normal.
2c. Higher optical density means a higher refractive index ($n$).
2d. The symbol for the refractive index is $n$.
Total Internal Reflection (TIR)
3a. The critical angle is the angle of incidence producing 90° refraction.
3b. If the angle of incidence is greater than the critical angle, total internal reflection occurs.
3c. Uses of TIR include: fiber optics and binoculars.
Speed of Light and Density
4a. The speed of light in a vacuum (air approximation) is $c = 3.00 \times 10^8 \text{ m/s}$.
4b. Higher optical density slows light; lower density speeds it up.
4c. Light moving from high $\to$ low density bends away from the normal.
4d. Light moving from low $\to$ high density bends toward the normal.
Lens Characteristics
5. Converging Lens (thicker in the middle):
- Beyond $2F$: Smaller, inverted, real image.
- At $2F$: Same size, inverted, real image.
- Between $F$ and $2F$: Larger, inverted, real image.
- Inside $F$: Larger, upright, virtual image.
Uses: magnifiers, cameras, eyes, microscopes.
Diverging Lens (thinner in the middle): Always produces a smaller, upright, virtual image. Used for myopia correction and door peepholes.
Real vs. Virtual Images
6. Real images form when rays actually meet; they are inverted and projectable. Formed by concave mirrors and converging lenses.
Virtual images form when rays only appear to meet; they are upright. Formed by plane/convex mirrors and diverging lenses.
The Human Eye Structure and Vision
7a. Eye Diagram Labels:
- Cornea: Front surface.
- Pupil: Light opening.
- Lens: Focuses light.
- Ciliary Muscles: Change lens shape.
- Retina: Image forms here.
- Optic Nerve: Transmits signal to the brain.
7b. Function Details: The iris controls pupil size; ciliary muscles adjust lens curvature; cones detect color and detail; rods detect low light and motion.
8. We do not perceive inverted images because the brain automatically flips them upright.
Common Vision Defects and Corrections
9. Vision Defects:
- Myopia (Nearsightedness): Eye too long; image forms in front of the retina $\to$ corrected with a diverging lens.
- Hyperopia (Farsightedness): Eye too short; image forms behind the retina $\to$ corrected with a converging lens.
- Presbyopia: Lens stiffens with age $\to$ requires a converging reading lens.
- Astigmatism: Uneven cornea $\to$ corrected with a cylindrical lens.
Optical Instruments
10a. The eye functions similarly to a camera: the lens focuses, the iris controls light entry, the retina acts as the sensor, and it forms inverted images.
10b. A compound microscope uses two converging lenses to produce a magnified virtual image.
10c. A magnifying glass (simple magnifier) requires the object to be placed inside $F$ to produce a large, upright, virtual image.
Selected Optical Calculations
Calculations:
- Refractive Index: $n = c/v = (3.00 \times 10^8) / (2.04 \times 10^8) = 1.47$.
- Speed in Medium: $v = c/n = (3.00 \times 10^8) / 1.46 = 2.05 \times 10^8 \text{ m/s}$.
- Magnification: $m = h_i/h_o = 58/19 = 3.05$.
- Diverging Lens (Finding Object Distance): $f = –29 \text{ cm}$, $d_i = –13 \text{ cm} \to 1/f = 1/d_o + 1/d_i \to d_o = 23.6 \text{ cm}$.
- Converging Lens (Finding Image Distance): $f = 34 \text{ cm}$, $d_o = 45 \text{ cm} \to 1/d_i = 1/f – 1/d_o \to d_i = 139 \text{ cm}$.
- Diverging Lens (Finding Focal Length): $m = 12/27 = 0.444$; $d_o = 25 / 0.444 = 56.3 \text{ mm}$; $1/f = 1/d_o + 1/d_i \to f \approx –45 \text{ mm}$.