Reflection of Light

Light

Light is a form of energy that is essential for our ability to perceive the world around us. Our ability to see and perceive the beauty of the world relies heavily on the presence of light. It enables us to engage in various visual activities like reading, viewing images, and watching television and movies.

The Characteristics and Behavior of Light

1. Light Travels in Straight Lines: Light travels in straight lines, as evidenced by the formation of sharp shadows cast by opaque objects.
2. Nature of Light: Light exhibits dual characteristics, which have led to two main theories about its nature: the wave theory and the particle theory.
3. Wave Theory of Light: According to the wave theory, light consists of electromagnetic waves that can propagate without a material medium. Visible light waves have very small wavelengths and travel at extremely high speeds, such as 3 × 108 m/s in a vacuum.
4. Particle Theory of Light: The particle theory suggests that light is composed of particles called photons, which travel in straight lines at high speeds. This theory helps explain phenomena like reflection, refraction, and the casting of shadows.
5. Combining Wave and Particle Models: Over the years, experiments in physics have demonstrated that light possesses both wave-like and particle-like properties, depending on the context. Different phenomena of light, such as diffraction and interference, are explained by wave theory, while reflection and refraction are better understood through particle theory.

Reflection of Light

Reflection of light is a fundamental phenomenon in optics where light waves encounter a surface and bounce back into the same medium. This process is responsible for our ability to see objects, as we perceive the light that is reflected from them.

Types of Reflection

Regular Reflection

1. Occurs on smooth and polished surfaces like mirrors or calm water.
2. Parallel incident rays of light remain parallel even after reflection and travel in one direction.
3. Provides a clear and distinct reflection.
4. The angle of incidence is equal to the angle of reflection.
5. Regular reflection forms sharp and well-defined images of objects, as seen in mirrors.
6. Highly polished metal surfaces and still water surfaces also produce regular reflection.
7. A polished wooden table, for example, produces regular reflection.
8. Regular reflection can be explained by the fact that all particles on a smooth surface are facing in one direction, causing the angles of incidence and reflection to be the same for all incoming parallel rays.

Diffuse Reflection

1. Occurs on rough or uneven surfaces like paper, cardboard, walls, or unpolished metal objects.
2. Parallel incident rays of light do not remain parallel after reflection; they scatter in various directions.
3. Results in a less defined and hazy reflection, often referred to as scattering.
4. No distinct image is formed due to diffuse reflection.
5. Rough surfaces scatter light in all directions because the angles of incidence and reflection vary for different particles.
6. Diffuse reflection is not due to the failure of the laws of reflection but is caused by surface irregularities on objects.
7. Most objects around us, which have rough surfaces, cause diffuse reflection and scatter light in all directions, making them visible to us.
8. Examples of diffuse reflection include a rough wall or a cinema screen.

Laws of Reflection

The First Law of Reflection

1. The incident ray, reflected ray, and the normal all lie on the same plane.
2. Incident ray: The incoming ray of light.
3. Reflected ray: The ray of light that bounces off the surface.
4. Normal: An imaginary line perpendicular to the surface where the light hits.
5. This law ensures that these three elements exist within the same flat surface or plane.

The Second Law of Reflection

1. The angle of incidence (∠i) is always equal to the angle of reflection (∠r).
2. Angle of incidence: The angle between the incident ray and the normal.
3. Angle of reflection: The angle between the reflected ray and the normal.
4. This law states that if a ray of light strikes a surface at a certain angle, the angle at which it reflects off the surface will be exactly the same

Images

An image is an optical appearance created when light rays from an object are reflected by a mirror or refracted through a lens. When we look into a mirror, what we see is actually a reflection of an object, and this optical appearance is termed an "image." For example, when you look into a mirror, you see the image of your face.
Images are of two types: real images and virtual images.

Real Images

1. A real image is one that can be projected onto a screen.
2. Real images are formed when light rays from an object physically converge at a point after reflecting off a mirror or passing through a lens.
3. In a cinema hall, the images of actors and actresses on the screen are real images.
4. Real images can be formed by concave mirrors and convex lenses.

Virtual Images

1. A virtual image cannot be projected onto a screen.
2. Virtual images can only be observed by looking into a mirror or a lens.
3. For instance, the image of your face in a plane mirror is a virtual image.
4. Virtual images are also referred to as unreal images because they are optical illusions.
5. Virtual images are formed when light rays from an object appear to meet at a point when extended backwards (but they do not actually converge) after reflecting off a mirror or passing through a lens.
6. Plane mirrors always produce virtual images, as do convex mirrors.

Image Formation by a Plane Mirror

Image formation by a plane mirror involves the reflection of light from the mirror's smooth and flat surface.

When light falls onto the smooth surface of a plane mirror, it follows the laws of reflection. These laws state that the angle of incidence (the angle between the incident ray of light and the normal to the mirror's surface) is equal to the angle of reflection (the angle between the reflected ray and the normal). This reflection of light occurs at each point on the mirror's surface.

Characteristics of Image Formed by a Plane Mirror

1. Virtual Image: The image formed in a plane mirror is virtual, which means it is not a real object but an optical illusion created by the reflected light rays. These rays of light appear to diverge from behind the mirror, giving the impression that there is an image located there. However, there is no physical object behind the mirror; it's a virtual image.
2. Distance and Size: The virtual image appears to be at the same distance behind the mirror as the actual object is in front of it. If you are standing 2 metres away from the mirror, your virtual image will seem to be 2 metres behind the mirror. The size of the virtual image is also the same as the actual object. If you are 1.7 metres tall, your virtual image will also be 1.7 metres tall.
3. Lateral Inversion: The image formed by a plane mirror is laterally inverted, which means that the left and right sides of the image appear reversed compared to the actual object. For example, if you raise your right hand in front of the mirror, the image shows it as the left hand, and vice versa. This lateral inversion creates a horizontal flip in the image.
4. Upright Image: The virtual image in a plane mirror is always upright, maintaining the same orientation as the actual object. If you stand upright in front of the mirror, your image will also appear upright.
5. Cannot Be Projected: The virtual image formed by a plane mirror cannot be projected onto a screen or captured on a surface. It exists only as an optical illusion and cannot be focused or touched.

Spherical Mirrors

Spherical mirrors are curved mirrors that have a reflective surface shaped like a part of a hollow sphere. These mirrors are used to reflect and focus light in various optical devices. There are two main types of spherical mirrors: concave mirrors and convex mirrors.

1. Concave Mirror

1. Reflecting Surface: The reflecting surface of a concave mirror is the inner, curved surface (bent inward), and it is where the reflection of light occurs.
2. Usage: Concave mirrors are commonly used in applications like makeup mirrors, shaving mirrors, and as reflectors in headlights.
3. Example: The inner, shining surface of a steel spoon serves as an example of a concave mirror.

2. Convex Mirror

1. Reflecting Surface: The reflecting surface of a convex mirror is the outer, curved surface (bulging outward), and it is where the reflection of light takes place.
2. Usage: Convex mirrors are often used as rear-view mirrors in vehicles and security mirrors in stores to provide a wider field of view.
3. Example: The backside of a shiny steel spoon demonstrates a convex mirror surface.

Important Terms Associated with Spherical Mirrors

1. Centre of Curvature (C): The centre of curvature of a spherical mirror is the centre of the imaginary hollow sphere from which the mirror's curved surface is derived. It is represented by the letter 'C.' In the case of a concave mirror, the centre of curvature is in front of the mirror, while for a convex mirror, it is behind the mirror.
2. Radius of Curvature (R): The radius of curvature of a spherical mirror is the distance from the centre of curvature (C) to the surface of the mirror. It is represented by 'R.'
3. Pole (P): The pole of a spherical mirror is the midpoint of its reflective surface. It is represented by 'P' and is the geometric centre of the mirror.
4. Principal Axis: The principal axis is an imaginary straight line that passes through the centre of curvature (C), the pole (P), and the principal focus (F) of the spherical mirror. It is a reference line for studying the behaviour of light rays in the mirror.
5. Principal Focus (F): The principal focus of a spherical mirror is a point on the principal axis where parallel rays of light either converge (in the case of a concave mirror) or appear to diverge (in the case of a convex mirror). The focus is represented by 'F.'
6. Focal Length (f): The focal length of a spherical mirror is the distance between its pole (P) and its principal focus (F). It is represented by 'f.'
7. For a concave mirror, the principal focus (F) is real and located in front of the mirror. In contrast, for a convex mirror, the principal focus (F) is virtual and situated behind the mirror.
   The relationship between the radius of curvature (R) and the focal length (f) of a spherical mirror is given by the equation:
   R = 2f
   This equation states that the focal length (f) is half the magnitude of the radius of curvature (R).

Rules for Obtaining Images Formed by Concave Mirrors

In the context of concave mirrors, there are four rules or principles that are commonly used to determine the position and characteristics of the images formed. These rules describe the behaviour of light rays as they interact with concave mirrors and help in understanding how images are produced.

1. Rule 1: A ray of light that is parallel to the principal axis of a concave mirror will pass through the focal point (F) after reflection from the mirror. This ray appears to converge at the focal point. In other words, if you draw a line parallel to the principal axis that strikes the mirror's surface, it will be reflected through the focal point.



2. Rule 2: A ray of light that passes through the centre of curvature (C) of a concave mirror will be reflected back along the same path. This is because the ray strikes the mirror's surface normally or perpendicularly. The angle of incidence and the angle of reflection are both zero degrees in this case. As a result, the reflected ray retraces its path.



3. Rule 3: A ray of light that passes through the focal point (F) of a concave mirror before striking the mirror will become parallel to the principal axis after reflection. This means that if you direct a ray of light through the focal point toward the mirror's surface, it will be reflected parallel to the principal axis. Rule 3 is essentially the reverse of Rule 1.



4. Rule 4: A ray of light that is incident at the pole (P) of a concave mirror will be reflected back at an angle equal to the angle of incidence. In other words, the angle of reflection (r) will be equal to the angle of incidence (i). When a ray of light strikes the mirror at the pole, it is reflected symmetrically with respect to the principal axis.

Formation of Images by Concave Mirror

The formation of different types of images by a concave mirror depends on the position of the object relative to the mirror. Concave mirrors are curved mirrors with an inward-curved reflective surface. They can produce real or virtual, upright or inverted, and magnified or diminished images based on where the object is located.

Primary cases of image formation by a concave mirror based on the object's position are:

Case 1

Object Between the Pole (P) and the Focus (F)
When the object is placed between the pole (P) and the focus (F) of the concave mirror, a virtual and magnified image is formed behind the mirror. Light rays diverge from the virtual image location, and no real light converges there.

Image Position: Behind the mirror
Image Type: Virtual
Image Orientation: Erect (upright)
Image Size: Enlarged (magnified)

Case 2

Object at the Focus (F)
When the object is placed exactly at the focus (F) of the concave mirror, the reflected rays become parallel and appear to converge at infinity. A real, highly magnified, and inverted image is formed, but it cannot be captured on a screen due to its infinite distance.

Image Position: At infinity
Image Type: Real
Image Orientation: Inverted
Image Size: Highly magnified

Case 3

Object Between the Focus (F) and the Center of Curvature (C)
When the object is positioned between the focus (F) and the centre of curvature (C), a real and magnified image is formed beyond the centre of curvature. The image is inverted, and it's larger than the object.

Image Position: Beyond the centre of curvature (C)
Image Type: Real
Image Orientation: Inverted
Image Size: Enlarged (magnified)

Case 4

Object at the Center of Curvature (C)
Placing the object at the centre of curvature results in a real, inverted image that is the same size as the object. The image forms exactly at the centre of curvature of the mirror.

Image Position: At the centre of curvature (C)
Image Type: Real
Image Orientation: Inverted
Image Size: Same size as the object

Case 5

Object Beyond the Center of Curvature (C)
When the object is positioned beyond the centre of curvature, a real and diminished (smaller) image is formed between the centre of curvature and the focus. The image is still inverted.

Image Position: Between the centre of curvature (C) and focus (F)
Image Type: Real
Image Orientation: Inverted
Image Size: Diminished (smaller than the object)

Case 6

Object at Infinity
When the object is located at an infinite distance from the concave mirror (effectively at "infinity"), a real, highly diminished, and inverted image is formed at the focus of the mirror.

Image Position: At the focus (F)
Image Type: Real
Image Orientation: Inverted
Image Size: Highly diminished (much smaller than the object)

Uses of Concave mirrors

Concave mirrors are versatile optical devices that find uses in different fields and everyday life.

1. Shaving and Makeup Mirrors: Concave mirrors are used as shaving and makeup mirrors because they produce enlarged and erect images when the face is within the focus. This makes it easier to see finer details and achieve precise grooming.
2. Dentistry: Dentists use concave mirrors to examine the teeth of patients. The mirrors produce enlarged images of the teeth, aiding in the detection of dental issues.
3. Lighting: Concave mirrors are employed in torches, vehicle headlights, and searchlights. Placing a light source (bulb) at the focus of a concave reflector generates a powerful, parallel beam of light, which is useful for illuminating distant objects or areas.
4. Medical Examination: Doctors use concave mirrors as head mirrors to focus light from a lamp onto specific body parts, such as the eyes, ears, nose, or throat, during medical examinations.
5. Television Dish Antennas: Concave dishes are used in satellite television (TV) dish antennas to receive TV signals from communication satellites. The concave dish collects and focuses signals onto an antenna, ensuring a strong signal for television reception.
6. Solar Energy: Large concave mirrors are utilised in solar energy applications. They focus sunlight onto a specific point, such as a solar furnace, which generates extremely high temperatures for various industrial processes like melting metals or producing steam for electricity generation.

Rules for Obtaining Images Formed by Convex Mirrors

The formation of images by convex mirrors is explained by certain rules and principles that help determine the position, nature, and size of the images. These rules are essential for constructing ray diagrams for convex mirrors. Convex mirrors have their focus and centre of curvature behind the mirror's reflective surface. As a result, all rays of light shown behind the convex mirror are virtual (unreal), and they are represented by dotted lines because real rays of light cannot pass through the mirror.

1. Rule 1: A ray of light parallel to the principal axis of a convex mirror appears to be coming from its focus after reflection from the mirror. In this case, the reflected ray is divergent, and when extended backwards, it appears to originate from the focus located behind the mirror.



2. Rule 2: A ray of light travelling towards the centre of curvature of a convex mirror is reflected back along the same path. This occurs because the incident ray is normal (perpendicular) to the mirror's surface at the point of reflection.



3. Rule 3: A ray of light directed towards the focus of a convex mirror becomes parallel to the principal axis after reflection. The reflected ray is parallel to the principal axis and diverges away from the focus.



4. Rule 4: A ray of light incident at the pole of a convex mirror is reflected back, making the same angle with the principal axis. The angle of incidence equals the angle of reflection. This rule applies when the incident ray is directed toward the pole of the convex mirror.

Formation of Images By Convex Mirror

The formation of an image by a convex mirror depends on the position of the object. In both cases, whether the object is between the pole and infinity or at infinity, the image is always formed behind the convex mirror, and it is virtual, erect, and diminished.

Case 1

When the Object is Placed Between the Pole (P) and the Infinity

Position of the Object: The object is anywhere between the pole (P) of the convex mirror and infinity.
Position of the Image: The image is formed behind the convex mirror, between the pole (P) and the focus (F).
Size of the Image: The image is diminished, meaning it is smaller in size compared to the object.
Nature of the Image: The image is virtual and erect.

Case 2

When the Object is at Infinity

Position of the Object: The object is placed at a very far-off distance, or at infinity.
Position of the Image: The image is formed behind the convex mirror, exactly at the focus (F).
Size of the Image: The image is highly diminished, much smaller than the object.
Nature of the Image: The image is virtual and erect.

Uses of Convex Mirror

1. Enhanced Rear-View Mirrors: Convex mirrors are commonly used as rear-view mirrors in vehicles such as cars, trucks, and buses. They offer several advantages for drivers:
   They produce upright (erect) images of objects.
   Convex mirrors create highly diminished images, making it easier to see a wider area of the traffic behind the vehicle. This broader field of view is crucial for safe driving.
   In contrast, flat (plane) mirrors provide a narrower field of view, which can limit a driver's ability to observe surrounding traffic.
2. Shop Security Mirrors: Large convex mirrors find applications in enhancing security in retail stores. When strategically placed, these mirrors allow shop owners to monitor customers and detect potential theft or shoplifting activities more effectively.

Sign Convention for Spherical Mirrors

The New Cartesian Sign Convention is a set of rules used for measuring distances in ray diagrams involving spherical mirrors, which include both concave and convex mirrors.

According to the sign convention:

Origin Point: The origin (zero point) for measuring distances is taken at the pole (P) of the mirror.

Positive and Negative Directions:

1. Distances measured in the same direction as the incident light (from left to right) are considered positive.
2. Distances measured in the opposite direction to the incident light (from right to left) are considered negative.
3. Distances measured upward and perpendicular to the principal axis are positive.
4. Distances measured downward and perpendicular to the principal axis are negative.

Object Distance (u): Since objects are always placed to the left side of the mirror (in the path of incident light), the object distance (u) is always negative.

Image Distance (v):

1. For concave mirrors, the image can be formed either behind the mirror (on the right side) or in front of the mirror (on the left side).
2. If the image is formed behind the mirror (to the right side), the image distance (v) is positive.
3. If the image is formed in front of the mirror (to the left side), the image distance (v) is negative.
4. For convex mirrors, the image is always formed behind the mirror (on the right side), so the image distance (v) is always positive.

Focal Length (f):

1. The focal length of a concave mirror, being in front of the mirror on the left side, is considered negative (e.g., -10 cm).
2. The focal length of a convex mirror, being behind the mirror on the right side, is considered positive (e.g., +20 cm or just 20 cm).

Height of Objects: The height of an object, which is always placed above the principal axis in the upward direction, is considered positive.

Height of Images:

1. All virtual images are erect and formed above the principal axis, so the height of virtual images is positive.
2. All real images are inverted and formed below the principal axis, so the height of real images is negative.

Mirror Formula

The mirror formula is a fundamental equation in optics that relates the distance of an object from a curved mirror, the distance of the image formed by the mirror, and the focal length of the mirror. It is commonly used to calculate these parameters for concave and convex mirrors.

It is expressed as follows:

Where,
v = distance of the image from mirror
u = distance of the object from mirror
f = focal length of the mirror

Linear Magnification Produced by Mirrors

The linear magnification (m) is a measure of how much larger or smaller an image is compared to the object. It is given by the formula:

Here,
h2 represents the height of the image
h1 represents the height of the object

Using Object and Image Distances:

The magnification can also be calculated using the object distance (u) and image distance (v) from the mirror:

Here,
v is the image distance, and
u is the object distance.

Summary of Magnification:

1. A positive magnification (m > 0) indicates an upright image (virtual or real).
2. A negative magnification (m < 0) indicates an inverted image (real).
3. Magnification equal to 1 (m = 1) means the image is the same size as the object.
4. Magnification greater than 1 (m > 1) means the image is larger than the object.
5. Magnification less than 1 (0 < m < 1) means the image is smaller (diminished) than the object.