Light: Mirrors and Lenses

Chapter at a Glance

This chapter details the concepts of light reflection and refraction using plane/spherical mirrors and lenses. It introduces concave and convex spherical mirrors, detailing how they form erect/inverted and enlarged/diminished images depending on the object's distance. It details the laws of reflection (equality of angles of incidence and reflection; coplanarity of incident, reflected, and normal rays) and demonstrates that these laws apply to both plane and curved surfaces. The chapter then transitions to lenses, defining convex (converging) and concave (diverging) lenses, exploring the characteristics of images seen through them, and highlighting applications in eyeglasses, cameras, and microscopes.

Key Definitions & Terminology

• Spherical Mirror: A curved mirror whose reflecting surface forms part of an imaginary hollow sphere.
• Concave Mirror: A spherical mirror with an inner reflecting surface curved inwards (converges parallel light rays).
• Convex Mirror: A spherical mirror with an outer reflecting surface curved outwards (diverges parallel light rays).
• Incident Ray: The ray of light that strikes the reflecting surface.
• Reflected Ray: The ray of light that bounces back from the reflecting surface.
• Normal: An imaginary perpendicular line drawn to the reflecting surface at the point of incidence.
• Angle of Incidence ($i$): The angle formed between the incident ray and the normal.
• Angle of Reflection ($r$): The angle formed between the reflected ray and the normal.
• Converging: The gathering of parallel light rays towards a single point (focus) after reflection or refraction.
• Diverging: The spreading out of parallel light rays away from each other after reflection or refraction.
• Lens: A piece of transparent material (glass or plastic) with curved surfaces that refracts light to form images.
• Convex Lens: A lens that is thicker in the middle than at the edges (converging lens).
• Concave Lens: A lens that is thinner in the middle than at the edges (diverging lens).

Formulas, Rules & Properties

• Laws of Reflection:
• First Law: The angle of incidence ($i$) is equal to the angle of reflection ($r$):
  $$\angle i = \angle r$$
• Second Law: The incident ray, the normal to the mirror at the point of incidence, and the reflected ray all lie in the same plane.
• Spherical Mirror Image Characteristics:
• Concave Mirror:
  • Object close: Erect, enlarged (magnified), virtual.
  • Object far: Inverted, diminished (or enlarged depending on distance), real.
• Convex Mirror:
  • Object at any distance: Always erect, diminished, virtual.
• Lens Image Characteristics:
• Convex Lens:
  • Object close: Erect, enlarged (acts as a magnifying glass).
  • Object far: Inverted, diminished (or enlarged depending on distance), real.
• Concave Lens:
  • Object at any distance: Always erect, diminished, virtual.

Core Concepts & Topics

• Law Verification Experiments:
• First Law: A narrow light beam is shone from a comb-slit onto a plane mirror. Measuring $i$ and $r$ with a protractor shows $i \approx r$. If a beam falls along the normal, $i = 0^\circ$ and $r = 0^\circ$.
• Second Law: A sheet of paper is extended off a table. Projecting incident/reflected rays and bending the extended edge down causes the reflected ray to disappear from the bent portion. It reappears when flattened, showing they lie on the same plane.
• Spoon Analogy:
• Inner curved side: acts as a concave mirror (shows inverted image at normal distance).
• Outer bulged side: acts as a convex mirror (shows erect, diminished image).
• Common Mirror Applications:
• Concave: Headlights/torches (places source at focus to project parallel beams), dentist mirrors (enlarged erect view of teeth), reflecting telescopes.
• Convex: Side-view mirrors on vehicles (wide field of view, erect image, warning: "Objects in mirror are closer than they appear"), surveillance mirrors in stores, sharp road intersections.
• Solar Concentrators:
• Concave mirrors converge solar rays to a single hot spot. Used in solar cookers, solar heaters, and solar furnaces (which can melt steel).
• Simple Water Drop Lens:
• Placing a drop of water on a wax/oil-coated transparent strip forms a curved convex dome. Reading text through this drop magnifies letters, acting as a convex lens.
• Lenses in Daily Life:
• Eyeglasses (for vision correction), cameras (cellphone and camera lenses), microscopes, and telescopes.
• The human eye contains a flexible convex lens that changes shape to focus on near or far objects.
• Bhaskara II (Historical Astronomy):
• Over 800 years ago, Indian astronomers used shallow water bowls as plane mirrors to reflect starlight. By looking through tubes, they calculated celestial positions, demonstrating practical understanding of reflection.

Worked Examples

• Reflective Ray Angle (Page 166 Q1):
• Problem: A light ray is incident on a mirror. The angle made by the incident ray with the normal is $40^\circ$. What is the angle made by the reflected ray with the mirror?
• Solution:
  • According to the first law of reflection, $\text{angle of reflection } (r) = \text{angle of incidence } (i) = 40^\circ$.
  • The normal is perpendicular ($90^\circ$) to the mirror surface.
  • Therefore, the angle made by the reflected ray with the mirror surface is:
    $$\text{Angle} = 90^\circ - r = 90^\circ - 40^\circ = 50^\circ$$
• Incidence along the Normal (Page 167 Q5):
• Problem: When light is incident along the normal on a mirror, which statement is true?
• Solution: The angle of incidence is measured between the incident ray and the normal. Since the ray is aligned along the normal, the angle of incidence is $0^\circ$. The angle of reflection is also $0^\circ$, causing the light to reflect straight back along its path.
• Vehicle Side-View Mirrors (Page 168 Q10):
• Problem: Why are convex mirrors preferred for vehicle side-view mirrors?
• Solution: Convex mirrors always form erect and diminished images. The diminished size of the images allows the mirror to capture light from a much wider viewing angle (field of view) compared to a plane mirror of the same size. This helps drivers see a larger area of traffic behind them, improving safety.
• Refraction in a Tumbler (Page 169 Q12):
• Problem: A pencil is placed behind a glass tumbler filled halfway with water. Why does the shape of the pencil appear changed/bent when viewed through the water?
• Solution: This occurs due to the refraction (bending) of light. The cylindrical glass tumbler filled with water acts like a curved convex lens. As light rays travel from the pencil through the water and glass into the air, they bend due to the change in medium. This refraction shifts the apparent position of the pencil segments submerged in water, making the pencil look bent or broken.

Practical Activities & Experiments

• Demonstrating Convergence and Divergence: Uncover multiple slits of a comb and place it in front of a torch to project parallel light beams. Shine these beams onto a concave mirror and observe them gather together (converge). Shine them on a convex mirror and observe them spread apart (diverge).
• Concentrating Sunlight (Paper Burning): Hold a concave mirror facing the Sun. Position a piece of newspaper in front of it and adjust the distance until a sharp, bright, concentrated dot of sunlight is formed. Hold it steady for a few minutes; the paper will begin to smoke and burn due to concentrated heat energy. Repeat this using a convex lens, which converges the transmitted light rays.
• Water Drop Magnifier: Apply a thin layer of oil or wax to a clear plastic scale. Place a small drop of water on the spot using a dropper. Look down through the drop at a page of small text; the curved water surface acts as a convex lens, magnifying the text.