**CHAPTER 9: LIGHT – REFLECTION AND REFRACTION**
**SECTION 9.1: LAWS OF REFLECTION**
• Light travels in straight lines (shown by sharp shadows)
• A ray of light is the path along which light travels
• Reflection occurs when light bounces off a polished surface (like mirrors)
**Laws of Reflection (apply to ALL reflecting surfaces):**
**Plane Mirror Image Properties:**
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**SECTION 9.2: SPHERICAL MIRRORS**
**Definition:** Mirrors whose reflecting surfaces form part of a sphere | used in curved spoons, car headlights, shaving mirrors
**Two Types of Spherical Mirrors:**
**1. CONCAVE MIRROR (also called Converging Mirror)**
• Reflecting surface curves INWARD (faces center)
• Center of curvature (C) lies IN FRONT of mirror
• Converges parallel rays to a point (focusing effect)
• Used in: telescopes, car headlights, shaving mirrors, searchlights, solar cookers
**2. CONVEX MIRROR (also called Diverging Mirror)**
• Reflecting surface curves OUTWARD (bulges out)
• Center of curvature (C) lies BEHIND mirror
• Diverges parallel rays (spreads them out)
• Used in: rear-view mirrors, shop security mirrors, vehicle side mirrors
**Key Terms for Spherical Mirrors:**
• **Pole (P):** Center point of reflecting surface | lies ON the mirror surface
• **Center of Curvature (C):** Center of sphere of which mirror is a part | NOT on mirror surface | distance PC = R
• **Radius of Curvature (R):** Radius of the sphere | distance from P to C | SI unit = meter (m)
• **Principal Axis:** Straight line through P and C | perpendicular to mirror at P
• **Principal Focus (F):** Point where parallel rays (parallel to principal axis) converge after reflection in concave mirror OR appear to diverge from in convex mirror
• **Focal Length (f):** Distance from pole P to principal focus F | f = R/2 | SI unit = meter (m)
**DON'T CONFUSE:**
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**SECTION 9.3: IMAGE FORMATION BY SPHERICAL MIRRORS (Mirror Formula & Magnification)**
**Mirror Formula (applies to both concave and convex mirrors):**
$$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$
Where:
• f = focal length (m) | positive for concave, negative for convex
• u = object distance from pole (m) | always POSITIVE
• v = image distance from pole (m) | positive if image is real (in front), negative if virtual (behind)
**Magnification Formula:**
$$m = \frac{h_{image}}{h_{object}} = \frac{-v}{u}$$
Where:
• m = magnification (unitless)
• h = height of object/image
• Negative m = real inverted image
• Positive m = virtual erect image
• |m| > 1 = enlarged image
• |m| < 1 = diminished image
• |m| = 1 = same size image
**Sign Convention for Mirrors:**
**Image Formation by Concave Mirror (using ray diagrams):**
• **Object at ∞ (infinity):** Real, inverted, point-sized image at F
• **Object beyond C:** Real, inverted, diminished image between F and C
• **Object at C:** Real, inverted, same-size image at C
• **Object between C and F:** Real, inverted, magnified image beyond C
• **Object at F:** No image formed (rays emerge parallel) OR Image at infinity
• **Object between F and P:** Virtual, erect, magnified image behind mirror
**Image Formation by Convex Mirror:**
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**SECTION 9.4: REFRACTION OF LIGHT**
**Definition:** Bending of light when it travels from one medium to another medium of different optical density
**Cause of Refraction:** Change in speed of light when entering different medium
**Laws of Refraction (Snell's Law):**
$$n_1 \sin(i) = n_2 \sin(r)$$
Where:
• n₁ = refractive index of first medium
• n₂ = refractive index of second medium
• i = angle of incidence (from normal)
• r = angle of refraction (from normal)
**Refractive Index (n):**
$$n = \frac{c}{v}$$
Where:
• c = speed of light in vacuum = 3 × 10⁸ m/s
• v = speed of light in medium (m/s)
• n is dimensionless (no units)
• n ≥ 1 (always)
• n(vacuum) = 1, n(air) ≈ 1, n(water) ≈ 1.33, n(glass) ≈ 1.5, n(diamond) ≈ 2.42
**Relative Refractive Index:**
$$n_{2,1} = \frac{n_2}{n_1} = \frac{v_1}{v_2}$$
**Behavior of Light During Refraction:**
• Speed DECREASES
• Light bends TOWARD normal
• Angle of refraction < Angle of incidence
• Speed INCREASES
• Light bends AWAY from normal
• Angle of refraction > Angle of incidence
**Critical Angle & Total Internal Reflection:**
• **Critical Angle (θc):** Angle of incidence in denser medium at which refracted ray grazes along interface (r = 90°)
$$\sin(θ_c) = \frac{n_2}{n_1}$$ (where n₁ > n₂, light going from denser to rarer)
• **Total Internal Reflection:** When angle of incidence > critical angle, light reflects back completely into denser medium (no refraction occurs)
• Conditions: Light traveling from denser to rarer medium AND angle > critical angle
• Used in: optical fibers, diamond brilliance, prisms
**DON'T CONFUSE:**
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**SECTION 9.5: LENSES (Convex & Concave)**
**Definition:** Transparent optical device with curved surfaces that refract light
**Types of Lenses:**
**1. CONVEX LENS (Converging Lens)**
• Thicker at CENTER, thinner at edges
• Acts as converging lens (brings parallel rays to focus)
• Focal length is POSITIVE
• Used in: magnifying glasses, cameras, projectors, microscopes, telescopes, human eye
**2. CONCAVE LENS (Diverging Lens)**
• Thinner at CENTER, thicker at edges
• Acts as diverging lens (spreads parallel rays)
• Focal length is NEGATIVE
• Used in: peepholes, some eyeglasses for myopia
**Lens Formula (same as mirror formula):**
$$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$
**Magnification by Lens:**
$$m = \frac{h_i}{h_o} = \frac{v}{u}$$
**Power of Lens:**
$$P = \frac{1}{f(in\ m)}$$ (in Diopters, D)
• Convex lens: P > 0 (positive power)
• Concave lens: P < 0 (negative power)
**Image Formation by Convex Lens:**
**Image Formation by Concave Lens:**
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**SECTION 9.6: DISPERSION OF LIGHT**
**Definition:** Splitting of white light into its component colors due to different refraction angles for different wavelengths
**Cause:** Different colors have different wavelengths → different refractive indices in a medium → different speeds → different bending angles
**Color Sequence (VIBGYOR):** Violet, Indigo, Blue, Green, Yellow, Orange, Red
• Violet: Shortest wavelength, most refracted, bends most toward normal
• Red: Longest wavelength, least refracted, bends least toward normal
**Examples:**
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**IMPORTANT DIAGRAMS TO REMEMBER:**
1. **Concave Mirror Ray Diagram:** Three principal rays
2. **Convex Mirror Ray Diagram:** Three principal rays
3. **Convex Lens Ray Diagram:** Three principal rays
4. **Prism Dispersion:** White light enters one face, splits into spectrum exiting
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**REAL-LIFE APPLICATIONS:**
• **Concave Mirror:** Shaving mirrors (magnified virtual image), car headlights (parallel beam), searchlights, solar cookers, reflecting telescopes
• **Convex Mirror:** Rear-view mirrors in vehicles, shop security mirrors, street lamps
• **Convex Lens:** Camera (real image on film), projector (real image on screen), microscope (magnified real image), telescope (magnified distant objects)
• **Concave Lens:** Eyeglasses for short-sightedness (myopia), peepholes in doors
• **Prism:** Separating light into colors, optical instruments
• **Optical Fibers:** Uses total internal reflection for long-distance communication
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**COMMON EXAM MISTAKES TO AVOID:**
Q1. A student performs Activity 9.2 with a concave mirror and focuses sunlight onto a paper sheet, creating a small bright spot. If the student moves the paper further away from the mirror, what will happen to the bright spot?
Answer: B — When paper is moved beyond the focal point of a concave mirror, the reflected rays begin to diverge. The spot does not disappear; it becomes larger and dimmer (unfocused). Disappearance (option A) is incorrect; the light is still there but spread over a larger area.
Q2. A person stands 25 cm in front of a large concave mirror with a radius of curvature of 100 cm. Based on the relationship between object distance and focal length, where will the image form?
Answer: D — With radius of curvature 100 cm, focal length f = 50 cm. The object is at u = 25 cm, which is less than f (object between pole and focal point). Using 1/v = 1/f - 1/u = 1/50 - 1/25 = -1/50, so v = -50 cm. The negative sign indicates the image is behind the mirror (virtual, erect, and magnified). Option A is wrong (real images need u > f), B and C require u beyond focal point.
Q3. A convex mirror is installed on a road curve as a safety mirror. A car approaching the mirror appears smaller than its actual size. Why does the convex mirror provide a wider field of view compared to a plane mirror?
Answer: A — The diverging nature of convex mirrors creates virtual images of a wider area; option B is false as size is arbitrary, and option C misunderstands the law of reflection which applies equally to all surfaces.
Q4. A student observes that when she looks at her face in the inner (concave) surface of a shining spoon held close to her face, the image appears upright and magnified. When she moves the spoon away slowly, at what point does the image suddenly invert and become real?
Answer: B — At the focal point (u = f), the image forms at infinity; beyond this point (u < f), the image becomes real and inverted; option A is incorrect as the image inverts before reaching the center of curvature.
Q5. During an experiment, a candle is placed 20 cm in front of a concave mirror of focal length 10 cm. A student calculates using the mirror formula and finds the image distance to be 20 cm. What type of image is formed and where?
Answer: A — Using 1/f = 1/u + 1/v: 1/10 = 1/20 + 1/v gives v = 20 cm, placing the image at the centre of curvature with magnification m = 1, forming a real inverted image of equal size; option C is a common wrong application of mirror rules.
Q6. Assertion (A): When a concave mirror is used as a shaving mirror, it is held close to the face so that the face lies between the pole and the focal point. Reason (R): In this region, a concave mirror always forms a virtual, erect, and magnified image. Choose the correct option:
Answer: A — Between P and F of a concave mirror, the image is always virtual, erect, and magnified, making it ideal for shaving; the reason correctly explains why this position is chosen.
Q7. Assertion (A): A convex mirror always forms a virtual image regardless of the object's position. Reason (R): The diverging nature of a convex mirror causes reflected rays to appear to originate from a point behind the mirror. Choose the correct option:
Answer: A — Convex mirrors always diverge rays, creating virtual images at any object position; the reason correctly explains this behavior.
Q8. Assertion (A): The principal axis of a spherical mirror is perpendicular to the mirror's surface at the pole. Reason (R): The principal axis passes through both the pole and the centre of curvature of the mirror. Choose the correct option:
Answer: B — Both statements are true: the principal axis is normal to the mirror at the pole and passes through P and C; however, reason R describes the definition of the principal axis rather than explaining why it is perpendicular.
Q9. In an experiment, a student places objects at different distances from a concave mirror and measures image distances. The student observes that as the object moves from the center of curvature toward the focal point, the image distance increases from equal to the object distance toward infinity. What does this observation reveal about the mirror?
Answer: A — The mirror formula 1/f = 1/u + 1/v explains that as u decreases (object approaches F), v increases, consistent with the observation; option B wrongly suggests focal length changes, which is a property of the mirror itself.
Q10. A laboratory experiment involves comparing images formed by a plane mirror and a concave mirror when an object is placed 30 cm away. The student notes that the plane mirror shows a virtual image at 30 cm behind, while the concave mirror (f = 15 cm) shows a real, inverted image at 30 cm in front. What is the key difference in how these mirrors bend light paths?
Answer: A — Concave mirrors converge rays toward the focal point to form real images for objects beyond F; plane mirrors reflect parallel rays creating virtual images; option B is incorrect as light absorption doesn't determine image type.
What is a ray of light?
A ray of light is a straight line representing the direction of light propagation from a source to an object.
State the laws of reflection of light.
The angle of incidence equals the angle of reflection, and the incident ray, reflected ray, and normal all lie in the same plane.
What is a spherical mirror?
A spherical mirror is a curved mirror whose reflecting surface forms part of a sphere, either concave (inward) or convex (outward).
Define the pole of a spherical mirror.
The pole (P) is the center point of the reflecting surface of a spherical mirror, lying on the surface itself.
What is the centre of curvature of a mirror?
The centre of curvature (C) is the center of the imaginary sphere of which the mirror's surface forms a part, located outside the mirror.
Define the radius of curvature.
The radius of curvature (R) is the radius of the sphere of which the reflecting surface forms a part, equal to the distance PC.
What is the principal axis of a mirror?
The principal axis is a straight line passing through the pole and centre of curvature of a spherical mirror, perpendicular to the mirror at the pole.
Where is the focus of a concave mirror formed?
The focus (F) of a concave mirror is the point on the principal axis where all light rays parallel to the axis converge after reflection.
How do concave and convex mirrors differ in position of centre of curvature?
In a concave mirror, the centre of curvature lies in front of the mirror, while in a convex mirror it lies behind the mirror.
What happens when you bring a concave mirror close to your face?
The image becomes magnified (enlarged) and remains upright and virtual when the object is between the pole and focus.
Define the following terms related to spherical mirrors: (a) Pole, (b) Centre of Curvature, (c) Radius of Curvature. [2 marks]
State the location and meaning of each term: Pole is center point on mirror surface (P), Centre of Curvature is center of the imaginary sphere (C, outside mirror), Radius of Curvature is the distance PC equal to R.
Explain with the help of a ray diagram why a concave mirror can concentrate sunlight at its focus. What is the relationship between focal length and radius of curvature? [3 marks]
Show that parallel rays incident on concave mirror converge at focus F after reflection (use law of reflection for each ray). State the relationship: f = R/2, meaning focal length equals half the radius of curvature because focus lies at midpoint between pole and centre of curvature.
Compare the images formed by a plane mirror, a concave mirror, and a convex mirror when an object is placed in front of them. Explain the differences in terms of the position of the centre of curvature and the type of image formed. How does the position of the object affect the image formed by a concave mirror? [5 marks]
For plane mirror: virtual, erect, same size, laterally inverted (no centre of curvature). For concave mirror: centre of curvature in front, can form real/virtual images depending on object position (beyond C → real diminished; at C → real same size; between C and F → real magnified; between F and P → virtual magnified). For convex mirror: centre of curvature behind, always forms virtual erect diminished image. Explain how changing object distance changes image nature in concave mirror using mirror formula and ray diagrams.
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