Light is a form of energy that travels in straight lines. It allows us to see the world. When light hits a surface, it can be reflected (bounced back), refracted (bent), or absorbed. Mirrors work by reflection; lenses work by refraction.
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Key Concepts and Definitions
- 1.Laws of Reflection:
- 2.The angle of incidence (i) equals the angle of reflection (r): angle i = angle r.
- 3.The incident ray, reflected ray, and normal all lie in the same plane.
Plane Mirror: Flat mirror. Forms a virtual, erect, laterally inverted image of the same size as the object, located as far behind the mirror as the object is in front.
- Spherical Mirrors: Curved mirrors — parts of a hollow sphere.
- Concave mirror: Reflecting surface curves inward (like a cave). Converges light. Used in torches, headlights, solar furnaces, dentist's mirror.
- Convex mirror: Reflecting surface curves outward. Diverges light. Forms virtual, erect, diminished image. Used in rear-view mirrors, street security mirrors.
Key terms — Spherical Mirrors: Centre of curvature (C), Radius of curvature (R), Pole (P), Principal axis, Principal focus (F), Focal length (f). Relationship: f = R/2.
Refraction: Bending of light as it passes from one medium to another due to change in speed. Light bends toward the normal when going from a rarer to denser medium; away from the normal when going from denser to rarer.
- Lenses: Transparent objects that refract light.
- Convex (converging) lens: Thicker at centre. Converges parallel light to a focal point. Used in magnifying glasses, cameras, eye glasses for far-sighted people.
- Concave (diverging) lens: Thinner at centre. Diverges light. Used in eye glasses for short-sighted people.
Mirror formula: 1/v + 1/u = 1/f (where v = image distance, u = object distance, f = focal length).
Magnification (m): m = -v/u. Positive m = erect image; negative m = inverted image. |m| > 1 means magnified.
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Worked Examples
An object is placed 30 cm in front of a concave mirror of focal length 15 cm. Find image distance and magnification.
Using 1/v + 1/u = 1/f: u = -30 cm, f = -15 cm.
1/v = 1/f - 1/u = 1/(-15) - 1/(-30) = -1/15 + 1/30 = -2/30 + 1/30 = -1/30.
v = -30 cm. Image is 30 cm in front of mirror (real, inverted). Magnification m = -v/u = -(-30)/(-30) = -1 (same size, inverted).
A convex mirror has a focal length of 20 cm. An object is placed 30 cm from it. Find image position.
For convex mirror, f = +20 cm, u = -30 cm.
1/v = 1/f - 1/u = 1/20 - 1/(-30) = 1/20 + 1/30 = 3/60 + 2/60 = 5/60. v = +12 cm (behind mirror — virtual, erect, diminished). This is why convex mirrors are used as rear-view mirrors.
A person stands 2 m from a plane mirror. How far is the person from their image?
Image is 2 m behind the mirror. Total separation = 2 + 2 = 4 m.
Why is a convex mirror preferred as a rear-view mirror?
It gives a wider field of view and always forms a virtual, erect, diminished image — the driver sees more road in one compact mirror.
A ray passes from air into glass — which way does it bend?
Glass is denser. Light slows down, so it bends toward the normal.
Why does a pool look shallower than it is?
Light from the bottom travels from water (denser) to air (rarer) and bends away from the normal, making the bottom appear closer — a refraction effect.
Object at centre of curvature (C) of a concave mirror — describe the image.
u = 2f, so image also forms at C: real, inverted, same size as object.
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Key Formulas
Key formulas
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Common mistakes
> In sign convention (New Cartesian), distances in front of the mirror are negative; distances behind are positive. Concave curves IN (cave) — converging; convex curves OUT — diverging.
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Summary
Reflection governs plane and spherical mirrors. Concave mirrors converge light and form image types that vary with object position. Convex mirrors always form virtual, erect, diminished images. Refraction explains lenses and apparent depth. The mirror formula and magnification formula allow quantitative image calculations.