Light: Mirrors and Lenses

CHAPTER 10: LIGHT: MIRRORS AND LENSES — COMPREHENSIVE NOTES

10.1 WHAT ARE SPHERICAL MIRRORS?

Definition of Spherical Mirrors

**Spherical mirrors** are mirrors whose reflecting surfaces are curved and shaped like a part of a hollow glass sphere. They are different from plane mirrors because their curved surfaces can bend and focus light differently.

The reflecting surface of a spherical mirror can be curved in two different ways:

Types of Spherical Mirrors

**1. Concave Mirror**

A **concave mirror** is a spherical mirror with a reflecting surface that curves inward (like the inside of a hollow sphere).

The reflecting surface faces inward

Also called a converging mirror

Representation: Shows a curved line with the center pointing inward

When you look at the inner surface of a shiny spoon, you see a concave mirror

**2. Convex Mirror**

A **convex mirror** is a spherical mirror with a reflecting surface that curves outward (like the outside of a hollow sphere).

The reflecting surface faces outward

Also called a diverging mirror

Representation: Shows a curved line with the center pointing outward

When you look at the outer surface of a shiny spoon, you see a convex mirror

How Spherical Mirrors Are Made

Spherical mirrors are NOT made by slicing a hollow glass sphere. Instead:

A flat piece of glass is ground and polished into a curved surface

A reflective coating (usually a thin layer of aluminum) is applied to make the surface reflective

If the coating is applied on the outer curved surface, it forms a **concave mirror**

If the coating is applied on the inner curved surface, it forms a **convex mirror**

Distinguishing Between Concave and Convex Mirrors

You can identify them by viewing from the side:

**Concave mirror**: The center curves inward toward you

**Convex mirror**: The center curves outward away from you

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10.2 WHAT ARE THE CHARACTERISTICS OF IMAGES FORMED BY SPHERICAL MIRRORS?

Images Formed by Concave Mirrors

When an object is placed at different distances from a concave mirror, the image changes:

**When object is close to the mirror (3-4 cm away):**

Image is **erect** (upright)

Image is **enlarged** (larger than the object)

Image is **virtual** (appears to be behind the mirror)

Shows lateral inversion (left appears right, right appears left)

**When object is moved farther away:**

Image becomes **inverted** (upside down)

Image size starts larger but gradually becomes **smaller**

Image becomes **real** (can be projected on a screen)

Eventually the image is smaller than the object

Images Formed by Convex Mirrors

A convex mirror always produces the same type of image regardless of object distance:

Image is always **erect** (upright)

Image is always **diminished** (smaller than the object)

Image is always **virtual** (appears to be behind the mirror)

Image size decreases slightly as object moves farther away

Shows lateral inversion

Comparison with Plane Mirrors

**Plane mirror** (from Class 7):

Always forms an erect image

Image is always the same size as object

Image is always virtual

Shows lateral inversion

**Spherical mirrors:**

Image size changes with distance

Concave mirror can form inverted images

Convex mirror always forms diminished erect images

Real-Life Applications of Spherical Mirrors

**Concave Mirrors:**

1. **Torches and flashlights**: The reflector inside is concave-shaped to concentrate light in one direction

2. **Car and scooter headlights**: The curved mirror focuses the light beam forward

3. **Dental mirrors**: Dentists use small concave mirrors to see an enlarged view of teeth inside the mouth

4. **Telescopes**: Modern reflecting telescopes use large concave mirrors as their main mirror to gather and focus light from distant stars

5. **Shaving mirrors**: Used to see an enlarged image of the face for shaving

**Convex Mirrors:**

1. **Side-view mirrors on vehicles**: Provide an erect, diminished image giving a wide field of view of the road behind. The warning "Objects in mirror are closer than they appear" is written because the convex mirror makes objects appear farther away than they actually are

2. **Road intersection mirrors**: Installed at sharp bends and intersections to help drivers see traffic from both directions and prevent collisions

3. **Store surveillance mirrors**: Hung in shops and large stores to monitor a wide area and detect theft

4. **Security mirrors**: Used in banks and offices to monitor large areas with a single mirror

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10.3 WHAT ARE THE LAWS OF REFLECTION?

Key Terms Related to Reflection

**Incident ray**: The ray of light that falls on the mirror's reflecting surface

**Reflected ray**: The ray of light that bounces back from the mirror's reflecting surface

**Normal**: An imaginary line drawn perpendicular (at 90°) to the reflecting surface at the point where the light ray hits it. This is drawn from the point of incidence outward.

**Point of incidence**: The exact point where the incident ray touches the mirror's surface

**Angle of incidence (i)**: The angle between the incident ray and the normal. It is measured from the normal to the incident ray.

**Angle of reflection (r)**: The angle between the reflected ray and the normal. It is measured from the normal to the reflected ray.

The Laws of Reflection

**Law 1: Angle of Incidence equals Angle of Reflection**

The angle of incidence is always equal to the angle of reflection.

**Mathematically: i = r**

This law is the most fundamental law of reflection and applies to ALL types of mirrors (plane, concave, and convex).

**Observation from Activity 10.4**: When you measure angles of incidence and reflection in an experiment with a plane mirror, you will find they are nearly equal (small differences due to measurement errors). If done with precision, i = r.

**Law 2: The Incident Ray, Normal, and Reflected Ray all lie in the Same Plane**

The incident ray, the normal at the point of incidence, and the reflected ray all exist in the same flat plane. None of them lies out of this plane.

**Why this matters**: If you bend a surface after reflection, the reflected ray disappears because it's no longer in the same plane as the incident ray.

Application of Laws to Different Mirrors

**In Plane Mirrors:**

Both laws are followed

Parallel rays remain parallel after reflection

**In Spherical Mirrors:**

**Concave Mirror:**

Each individual ray follows the laws of reflection at its point of incidence

However, multiple parallel rays converge (come together) after reflection

This happens because different rays hit the curved surface at different angles, so their normals point in different directions

The rays meet at a point called the **focus** or **focal point**

**Convex Mirror:**

Each individual ray follows the laws of reflection

Multiple parallel rays diverge (spread apart) after reflection

The reflected rays appear to come from a point behind the mirror called the virtual focus

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10.4 WHAT IS A LENS?

Definition of Lens

A **lens** is a piece of transparent material (usually glass or plastic) with curved surfaces that can bend light rays passing through it.

**Key difference from mirrors:**

Mirrors reflect light and you see images IN the mirror

Lenses refract (bend) light and you see objects THROUGH the lens

Lenses are transparent and allow light to pass through

Types of Lenses

**1. Convex Lens (Also called Converging Lens)**

A **convex lens** is thicker in the middle (at the center) and thinner at the edges.

**Representation:**

Drawn as two outward-bulging curves or as connected triangles pointing outward

Both surfaces curve outward

**Properties:**

Causes parallel rays to converge (come together)

Can magnify objects

Used in magnifying glasses

**2. Concave Lens (Also called Diverging Lens)**

A **concave lens** is thinner in the middle (at the center) and thicker at the edges.

**Representation:**

Drawn as two inward-curving curves or as connected triangles pointing inward

Both surfaces curve inward

**Properties:**

Causes parallel rays to diverge (spread apart)

Makes objects appear smaller

Used to correct certain vision problems

How Lenses Work

When light passes through a lens, it bends (refracts) because:

Light travels at different speeds in different materials

The curved surface causes light rays to bend at different angles

This bending causes rays to either converge or diverge

Real-Life Example: Water Drop as a Lens

A small drop of water on a curved surface acts like a simple convex lens. When you look through it at text on paper below, the text appears larger because the curved water surface bends the light rays to magnify the image.

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10.5 CHARACTERISTICS OF IMAGES FORMED BY LENSES

Images Formed by Convex Lenses

**When object is very close to the lens:**

Image is **erect** (upright)

Image is **enlarged** (magnified)

Image is **virtual** (cannot be projected on a screen)

Used in magnifying glasses

**When object is at moderate distance:**

Image is **inverted** (upside down)

Image is **enlarged**

Image is **real** (can be projected on a screen)

**When object is far from the lens:**

Image is **inverted** (upside down)

Image is **diminished** (smaller than object)

Image is **real** (can be projected on a screen)

**As object moves farther away:**

Image size decreases gradually

Image position moves closer to the lens

Images Formed by Concave Lenses

A concave lens always produces the same characteristics regardless of object distance:

Image is always **erect** (upright)

Image is always **diminished** (smaller than object)

Image is always **virtual** (cannot be projected on a screen)

The image appears to be on the same side of the lens as the object

Real-Life Applications of Lenses

**Convex Lenses:**

1. **Magnifying glasses**: Used to read small print or examine small objects with an enlarged view

2. **Camera lens**: Focuses light to form real, inverted, diminished images on film or sensors

3. **Projectors**: Focus light to project enlarged images on a screen

4. **Microscopes**: Multiple convex lenses work together to magnify tiny objects (bacteria, cells)

5. **Telescope**: Convex lenses gather and focus light from distant objects (stars, planets)

6. **Human eye**: The natural lens in your eye is convex and focuses light on the retina

7. **Reading glasses**: Used by people with presbyopia (age-related vision loss) to magnify text

**Concave Lenses:**

1. **Correcting myopia (nearsightedness)**: People who can see nearby objects clearly but cannot see distant objects use concave lenses to diverge light rays and correct vision

2. **Peepholes in doors**: Provide a wide field of view of the corridor or entrance

3. **Telescope eyepieces**: Some telescope designs use concave lenses

4. **Some camera viewfinders**: Help show a wider field of view

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KEY CONCEPTS AND DEFINITIONS SUMMARY

**Plane Mirror**: A flat reflecting surface that always forms an erect, same-size, virtual image with lateral inversion

**Concave Mirror**: A curved mirror that curves inward, can converge light rays, form enlarged or diminished images depending on object distance

**Convex Mirror**: A curved mirror that curves outward, diverges light rays, always forms diminished erect images

**Convex Lens**: Thicker at center, causes convergence of light, can magnify objects

**Concave Lens**: Thicker at edges, causes divergence of light, always diminishes objects

**Angle of Incidence (i)**: Angle between incident ray and normal

**Angle of Reflection (r)**: Angle between reflected ray and normal

**Normal**: Perpendicular line to mirror surface at point of incidence

**Focal Point/Focus**: Point where parallel rays meet after reflection from concave mirror or refraction through convex lens

**Virtual Image**: Image that cannot be projected on a screen (appears to be behind mirror or on same side as object for lens)

**Real Image**: Image that can be projected on a screen

**Lateral Inversion**: Left and right sides appear reversed (seen in all mirrors)

**Erect Image**: Image in same upright orientation as object

**Inverted Image**: Image turned upside down

**Magnified/Enlarged Image**: Image larger than object

**Diminished Image**: Image smaller than object

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IMPORTANT DIAGRAMS TO DRAW

Diagram 1: Concave and Convex Mirrors Representation

Draw concave mirror as a curved line with shading on the back showing it curves inward

Draw convex mirror as a curved line with shading on the back showing it curves outward

Label the reflecting surface and non-reflecting surface

Diagram 2: Angle of Incidence and Angle of Reflection

Draw a straight line representing the mirror surface

Draw a perpendicular line (normal) at the point of incidence

Draw an incident ray approaching the mirror at an angle

Draw a reflected ray leaving the mirror at an angle

Mark angle i between incident ray and normal

Mark angle r between reflected ray and normal

Show that i = r

Diagram 3: Parallel Rays on Different Mirrors

Plane mirror: Draw multiple parallel rays hitting the surface and reflect as parallel rays

Concave mirror: Draw multiple parallel rays hitting the surface and converge to a focus point

Convex mirror: Draw multiple parallel rays hitting the surface and diverge as if coming from a virtual focus behind the mirror

Diagram 4: Convex and Concave Lens Representation

Convex lens: Draw two outward-bulging curves meeting in the middle (thicker at center)

Concave lens: Draw two inward-curving curves meeting in the middle (thinner at center)

Label both surfaces

Diagram 5: Light Path Through Lenses

Convex lens: Draw parallel rays entering from left, bending inward, converging to a point on right

Concave lens: Draw parallel rays entering from left, bending outward, diverging as if from a point on left

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EXPERIMENTAL OBSERVATIONS AND CONCLUSIONS

**From Activity 10.1 (Metallic Spoon):**

Inner curved surface acts like concave mirror → inverted image

Outer curved surface acts like convex mirror → erect, diminished image

**From Activity 10.3 (Images in Mirrors):**

Concave mirror: Changes image characteristics based on distance

Convex mirror: Always produces consistent diminished erect image

**From Activity 10.4 (Angles of Reflection):**

When angles are measured carefully, angle of incidence = angle of reflection

This holds true even when incident ray angle is changed

**From Activity 10.5 (Plane of Reflection):**

When paper is bent, reflected ray disappears

When paper is flattened, reflected ray reappears

This proves incident ray, normal, and reflected ray lie in same plane

**From Activity 10.6 (Parallel Rays on Spherical Mirrors):**

Plane mirror: Parallel rays reflect as parallel rays

Concave mirror: Parallel rays converge after reflection

Convex mirror: Parallel rays diverge after reflection

**From Activity 10.7 (Converging Light):**

Concave mirror can concentrate sunlight to produce high heat

Can ignite paper and produce smoke

This concentration is used in solar energy applications

**From Activity 10.8 (Water Drop as Lens):**

Water drop has curved surface bulging outward = convex lens shape

Text below appears enlarged when viewed through water drop

Demonstrates that curved transparent surfaces can magnify objects

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CAUSE AND EFFECT RELATIONSHIPS

**Cause**: Object is very close to concave mirror

**Effect**: Erect, enlarged, virtual image forms

**Cause**: Object is far from concave mirror

**Effect**: Inverted, diminished, real image forms

**Cause**: Light ray falls on curved mirror surface at different points

**Effect**: Normal directions are different at each point, so reflected rays have different directions

**Cause**: Multiple parallel rays hit concave mirror at different points

**Effect**: Each ray reflects following law of reflection, but combined effect is convergence

**Cause**: Multiple parallel rays hit convex mirror at different points

**Effect**: Each ray reflects following law of reflection, but combined effect is divergence

**Cause**: Light passes through a curved transparent medium (lens)

**Effect**: Light rays bend (refract) due to change in speed of light in the material

**Cause**: Light rays bend inward through convex lens

**Effect**: Parallel rays converge; objects appear magnified when close to lens

**Cause**: Light rays bend outward through concave lens

**Effect**: Parallel rays diverge; objects always appear smaller

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REAL-LIFE CONNECTIONS AND APPLICATIONS

In Transportation

**Car headlights and taillights**: Concave mirrors direct light forward and backward

**Side-view mirrors**: Convex mirrors on vehicles for safety

**Street intersection mirrors**: Convex mirrors prevent accidents

In Healthcare

**Dental mirrors**: Concave mirrors used by dentists to examine teeth

**Surgical headlamps**: Concave mirrors for focusing light on surgical areas

**Correction glasses**: Convex lenses for hyperopia, concave lenses for myopia

In Astronomy

**Telescopes**: Large concave mirrors collect and focus starlight

**Observatories**: Use curved mirrors to observe celestial objects

In Daily Life

**Magnifying glasses**: Convex lenses for reading small print

**Peepholes**: Concave lenses in door viewers

**Store security mirrors**: Convex mirrors to monitor large areas

**Bathroom/shaving mirrors**: Concave mirrors for magnified view

In Modern Technology

**Cameras and smartphones**: Convex lenses to focus light for photos

**Projectors**: Convex lenses to enlarge images on screens

**Microscopes**: Multiple lenses to magnify tiny organisms and cells

In Energy

**Solar concentrators**: Concave mirrors concentrate sunlight for heating

**Solar furnaces**: Heat from concentrated sunlight used for industrial purposes

**Solar cookers**: Use mirrors to concentrate heat for cooking

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IMPORTANT POINTS TO REMEMBER

1. **Spherical mirrors** have curved reflecting surfaces and can be concave (curves inward) or convex (curves outward)

2. **Concave mirrors** can produce enlarged or diminished images depending on object distance; convex mirrors always produce diminished images

3. **The law of reflection** (i = r) applies to all mirrors including spherical mirrors

4. **Parallel rays** behave differently on different mirrors:

Plane mirror: Remain parallel

Concave mirror: Converge

Convex mirror: Diverge

5. **Lenses** are transparent and work by bending (refracting) light, unlike mirrors which reflect light

6. **Convex lenses** converge light and can magnify nearby objects; concave lenses diverge light and always diminish objects

7. **Real images** can be projected on a screen (inverted, from lenses or distant objects from concave mirrors); **virtual images** cannot be projected (erect)

8. **Safety warning on vehicle side mirrors** exists because convex mirrors make objects appear farther than they actually are

9. **Dental mirrors are concave** because they provide magnified view of teeth when held close to them

10. **All spherical mirrors follow laws of reflection** even though they cause parallel rays to converge or diverge

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SUMMARY TABLE: MIRROR AND LENS COMPARISON

| Property | Plane Mirror | Concave Mirror | Convex Mirror | Convex Lens | Concave Lens |

|----------|--------------|----------------|---------------|-------------|--------------|

| Shape | Flat | Curves inward | Curves outward | Thick center | Thin center |

| Light behavior | Reflects | Converges | Diverges | Converges | Diverges |

| Image (close object) | Erect, same size | Erect, enlarged | Erect, diminished | Erect, enlarged | Erect, diminished |

| Image (far object) | Erect, same size | Inverted, diminished | Erect, diminished | Inverted, diminished | Erect, diminished |

| Can form real image | No | Yes | No | Yes | No |

| Magnification | 1x | Variable | Always <1 | Variable | Always <1 |