Light – Reflection & Refraction: Comprehensive Study Notes

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Chapter Context: Light – Reflection & Refraction

What is Light?

• Light is a form of energy that enables the sensation of sight; it allows us to see objects around us.

Reflection of Light

• Reflection is the bouncing back of light rays into the same medium after striking a reflecting surface.

Laws of Reflection

1. The incident ray, the reflected ray and the normal to the reflecting surface at the point of incidence all lie in the same plane.

2. The angle of incidence $\theta<em>i$ is equal to the angle of reflection $\theta</em>r$.

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Important Terms (Reflection)

1. Incident Ray – Ray of light that strikes the reflecting surface.

2. Reflected Ray – Ray of light that bounces back after reflection.

3. Normal – Line drawn perpendicular to the reflecting surface at the point of incidence.

4. Angle of Incidence ($\theta_i$) – Angle between the incident ray and the normal.

5. Angle of Reflection ($\theta_r$) – Angle between the reflected ray and the normal.

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Plane Mirror Construction

• A plane mirror is a flat glass sheet coated with a reflecting layer (usually silver amalgam) on one side, protected by red paint.

• Why red paint?

  • Prevents oxidation of silver.

  • Absorbs stray light and stops transmission through the back surface.

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Image Formation by a Plane Mirror

• Incident rays reflect symmetrically to produce an image that appears to be behind the mirror.

• A simple ray diagram shows equal angles and equal object–image distances.

Concept of Real vs. Virtual Images

• Virtual Image (Fig-3): Reflected rays do not actually meet; they only appear to diverge from a point behind the mirror. Properties: erect, cannot be captured on a screen.

• Real Image (Fig-4): Reflected rays actually meet in front of the mirror. Properties: inverted, can be captured on a screen (e.g., projector).

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Properties of the Plane-Mirror Image

1. Virtual and erect.

2. Laterally inverted.

3. Object distance $=\,$ Image distance.

4. Object size $=\,$ Image size.

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Lecture-2 — Spherical Mirrors

Definition

• Mirrors whose reflecting surfaces are parts of a sphere.

Types & Uses

1. Concave Mirror (Converging)

   • Surface curved inward (like a cave).

   • Uses: torchlights, headlights, shaving/makeup mirrors, search lights.

2. Convex Mirror (Diverging)

   • Surface bulged outward.

   • Uses: rear-view mirrors, security mirrors.

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Key Geometrical Terms (Spherical Mirrors)

• Pole (P): Center of the reflecting surface.

• Centre of Curvature (C): Center of the sphere of which the mirror is a part. For concave it lies in front; for convex it lies behind the reflecting surface.

• Principal Axis: Imaginary line through $C, F,$ and $P$, perpendicular to the mirror surface.

• Principal Focus (F): Point where rays parallel to principal axis converge (concave) or appear to diverge from (convex). Lies between $C$ and $P$ for concave; behind the mirror for convex.

• Focal Length (f): Distance $PF$. Always $f = \frac{R}{2}$ where $R$ is the radius of curvature $PC$.

• Aperture: Effective diameter of the reflecting surface.

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Ray-Diagram Rules for Spherical Mirrors

1. A ray parallel to the principal axis passes through (concave) or appears to come from (convex) the focus.

2. A ray passing through the focus emerges parallel to the principal axis.

3. A ray passing through the centre of curvature reflects back along its original path (normal incidence).

4. An oblique ray incident at pole obeys the law of reflection with equal angles to the principal axis.

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Image Formation by a Concave Mirror

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Image Formation by a Convex Mirror

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Lecture-4 — Mirror Formula & Magnification

Sign Convention (Cartesian)

• Distances measured in the direction of incident light: positive.

• Distances opposite to incident light: negative.

• Heights above principal axis: positive; below: negative.

Mirror Formula

$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$
where

• $u$ = object distance (from pole)

• $v$ = image distance

• $f$ = focal length

Linear Magnification

$m = \frac{hi}{ho} = -\frac{v}{u}$
Signs indicate erect/inverted and virtual/real.

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Numerical Example (Concave Mirror)

Given: $R = +3\,\text{m}, \; u = -5\,\text{m}$
Focal length: $f = \frac{R}{2} = +1.5\,\text{m}$
Using mirror formula:
$\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{1.5} - \left(-\frac{1}{5}\right)$
$\Rightarrow v \approx +1.15\,\text{m}$ (image in front of mirror)
Magnification: $m = -\frac{v}{u} \approx 0.23$ (virtual, erect, smaller).

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Numerical Example 2

Given: $h_o = 4\,\text{cm},\; u = -25\,\text{cm},\; f = -15\,\text{cm}$ (convex mirror f>0, concave f<0; here negative indicates concave).
Find $v$ using mirror formula:
$\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = -\frac{1}{15} - \left(-\frac{1}{25}\right)$
$\Rightarrow v \approx -37.5\,\text{cm}$
Magnification: $m = -\frac{v}{u} \approx -1.5$
Image is inverted, enlarged, real.

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Lecture-5 — Refraction of Light

Definition

Refraction is the bending of light as it passes from one medium to another with different optical density due to change in speed.

Direction of Bending

1. From rarer to denser medium: bends toward the normal.

2. From denser to rarer medium: bends away from the normal.

Refraction through a Rectangular Glass Slab

• Light refracts twice:

  • Air → glass (toward normal).

  • Glass → air (away from normal).

• Emergent ray is parallel to incident ray but laterally displaced.

Refractive Index $n$

$n = \frac{c}{v}$ where $c$ is speed of light in vacuum, $v$ in medium.
Typical values: $n{\text{air}} \approx 1.0,$ $n{\text{water}} \approx 1.33,$ $n_{\text{glass}} \approx 1.5.$

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Lecture-6 — Lenses

Spherical Lens

A transparent medium bounded by two spherical surfaces (or one spherical and one plane).

Types

1. Convex Lens (Converging): Thicker at center; brings rays closer.

   • Forms real or virtual images depending on object position.

2. Concave Lens (Diverging): Thinner at center; spreads rays.

   • Always forms virtual, erect, diminished images.

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Ray-Diagram Rules for Lenses

1. Ray parallel to principal axis → after refraction passes through $F2$ (convex) or appears to come from $F1$ (concave).

2. Ray through (or directed toward) focus → emerges parallel to principal axis.

3. Ray through optical centre $O$ → continues undeviated.

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Image Formation by a Convex Lens

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Image Formation by a Concave Lens

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Sign Convention for Lenses

• Origin at optical centre $O$.

• Object distances ($u$) measured against incident light: negative.

• Image distances ($v$) measured in direction of emergent light: positive.

• Heights above principal axis: positive; below: negative.

Lens Formula

$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$

Linear Magnification (Lenses)

$m = \frac{hi}{ho} = \frac{v}{u}$
(Signs follow convention.)

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Numerical Example (Convex Lens)

Given: $f = +10\,\text{cm},\; u = -15\,\text{cm}$.
Lens formula: $\frac{1}{v} = \frac{1}{f} + \frac{1}{u}$
$\frac{1}{v} = \frac{1}{10} - \frac{1}{15} = \frac{3 - 2}{30} = \frac{1}{30}$
$v = +30\,\text{cm}$ (real, opposite side).
Magnification: $m = \frac{v}{u} = \frac{30}{-15} = -2$ (image inverted, twice size).

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Lecture-7 — Power of a Lens

Definition

Power ($P$) is the reciprocal of focal length (in metres):
$P = \frac{1}{f}$
Unit: Dioptre (D).

Sign Convention

• Convex lens: $f$ positive ⇒ $P$ positive (converging).

• Concave lens: $f$ negative ⇒ $P$ negative (diverging).

Applications

• Corrective lenses for myopia/hyperopia.

• Optical instrument design (microscopes, telescopes, cameras).

• Quick calculation of focal length from given power and vice-versa.

End of Notes