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 : When incident light is reflected in only one direction.

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: When incident light is reflected in different directions

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.
4. type of curved mirrors are spherical mirrors. Mirrors in which reflecting surface are spherical in shape, is known as spherical mirrors. Reflecting surface of a mirror can be curved inwards or curved outwards. The one which is curved inward is known as concave mirror and the one which curved outwards is known as convex mirror.

Some Important Terms

• Pole - The centre of the reflecting surface in a spherical mirror is a pole. It is represented by P.
• Centre of curvature - Reflecting surface in a spherical mirror has a centre, this is known as centre of curvature. Centre of curvature in convex mirror lies behind the mirror whereas in concave mirror, it lies in front of the mirror.
• Radius of curvature - The radius of the reflecting surface of the spherical mirror is known as radius of curvature. It is represented by R.
• Principal axis - Straight line passing through the pole and centre of curvature in a spherical mirror is known as principal axis.
• Principal focus - The reflected rays appear to come from a point on the principal axis, this is known as principal focus.
• Focal length - The distance between the pole and the principal focus in a spherical mirror is known as focal length and it is represented by f.
• Aperture- The diameter of the reflecting surface is defined as aperture.
• Note: Radius of curvature is twice the focal length (R=2f).

Representations of the images formed by Spherical Mirrors using Ray Diagrams

We draw the ray diagram to locate the image of an object formed. The intersection point of at least two reflected will give the position of image of the point object. The two rays that can be used to draw the ray diagram are-

• A ray parallel to the principal axis should pass through the focus after reflection in case of concave mirror, or appear to diverge in case of convex mirror.

• A ray passing through the focus of the concave mirror or directed towards the focus in case of convex mirror, should appear parallel to the principal axis after reflection.

• A ray which is passing through the centre of curvature in a concave mirror or directed in case of convex mirror, should reflect along the same path.

• A ray when incident obliquely to principal axis on a concave or convex mirror is also reflected obliquely.

Image formation by Concave Mirror

Fig. 3.  Ray diagram for the image formation by concave mirror

Table.1.  Nature, relative size and position of the image formed by concave mirror

Position, nature, and the size of the image formed by a concave mirror is dependent on the position of the object in relation to P, C and F. Image formed can be real or virtual. The image can also be magnified, diminished or even of the same size.

Uses of Concave Mirror

Used in search lights, torches, head lights of the vehicles. Also used in shaving mirrors. Used by dentists also to see larger image of the teeth. Other use in solar furnaces.

Image formation by Convex Mirror

Two positions of the object are considered while understanding the image formed by convex mirror. Either the object should be at infinity or at finite distance from the mirror. Formation of the image by the convex mirror are as follows-

Fig. 5. Ray diagram for the image formation by convex mirror

Table.2.  Nature, relative size and position of the image formed by convex mirror

Uses of Convex Mirror

They are used as rear-view mirrors. They are used to see the traffic behind. They are preferred as they give erect but diminished image.

Sign convention for reflection by spherical mirrors

New cartesian sign convention is used to give sign convention used for spherical mirrors. The conventions are as follows-

1. The object is always placed to the left of the mirror.

2. All distances parallel to the principal axis are measured from the pole of the mirror.

3. All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along – x-axis) are taken as negative.

4. Distances measured perpendicular to and above the principal axis (along + y-axis) will be taken as positive.

5. Distances measured perpendicular to and below the principal axis (along –y-axis) will be taken as negative.

Mirror formula and magnification

The distance of the object from its pole is known as object distance (u), whereas distance from the pole of the mirror is known as image distance (v). The mirror formula is given by-

It is applicable for spherical mirrors in all positions of the object.

Magnification

It is defined as relative extent to which an object is magnified in comparison to its object size.

Where m is the magnification, h_o is the height of the object and h_i is the height of the image. However, it is to be taken as negative for real images. A negative sign in the value of magnification indicates that the nature of the image is real. A positive sign in the value of the magnification indicates the virtual nature of the image.

Refraction of light

Bending of the light rays as it passes from one medium to another medium is known as refraction of light.

Laws of Refraction

• Incident ray, refracted ray and normal all lie in the same plane.
• The ratio of sine of angle of incidence to the sine of angle of refraction is constant. This law is also known as Snell’s law of refraction.

Refractive Index

When light passes from one medium to another medium, it changes its direction. The extent to which the direction changes is expressed in terms of refractive index. The value of refractive index is dependent on the speed of light in two media. v₁ is the speed of light in medium 1 and v₂ is the speed of light in medium 2. The refractive index of medium 2 with respect to medium 1 is represented as n₂₁.

If medium 1 is vacuum or air, then the refractive index of medium 2 with respect to vacuum is known as absolute refractive index of the medium.

Where c is the speed of light in air, v is the speed of light in other medium and n_m is the refractive index of the medium.

Refraction by Spherical Lenses

Lenses are defined as transparent materials which are bounded by two surfaces, out of which one or both can be spherical. When both the two spherical surfaces bulge outwards, it is known as convex lens. They converge the light rays. When the two spherical surfaces bulge inwards, they are known as concave lens. They are known as diverging lens. The centre of these spherical surfaces is known as centre of curvature, represented by C.

Any imaginary straight line passing through the centre of curvature of a lens is known as principal axis. The centre point is known as optical centre. The effective diameter of the spherical lens is known as aperture.

Image formation by lenses

Nature, relative size, and position of the image formed by convex lens are given below in the form of table-

Image formation in Lenses using Ray Diagrams

Rules for drawing the ray diagrams are as follows-

1. A ray of light which is parallel to the principal axis will pass through the principal focus after refraction from the convex lens.

2. A ray of light passing through principal focus, will emerge parallel to principal axis after refraction from the convex lens.

3. A light ray passing through optical centre will emerge out without any deviation.

Image formed by the Convex Lens for various positions of the object

Image formed by the Concave Lens

Sign convention for Spherical Lenses

Sign convention are used as similar for spherical mirrors. But the focal length of a convex lens is positive and that of concave lens in negative.

Lens formula and magnification

The lens formula is given as

Where, u is object distance, v is image distance and f is focal length.

The ratio of the height of an image to the height of an object is defined as magnification.

Magnification is represented by m, h₀ is the height of the object and h_i is the height of the image.

Power of a Lens

The degree of convergence or divergence of light rays is expressed in terms of power. So, the reciprocal of focal length is known as its power. It is represented by letter P. The power is given by-

P = 1/f

The SI unit of power is dioptre. It is represented by D. Power of concave lens is negative and power of convex lens is positive.

Handwritten Notes