Reflection of light at curved surfaces Part-2

Spherical Mirrors:

A Spherical mirror is a curved mirror whose one side is reflecting and the other side is a coated one. It is part of a hollow sphere.

The spherical mirror is classified into two types, they are concave mirror and convex mirror.

1.   Concave Mirror: A spherical mirror whose inner side is reflecting and the outer side is coated or silvered is called a concave mirror. A concave mirror is also referred to as Converging Mirror as it converges the light rays after reflection.

2.   Convex Mirror: A spherical mirror whose outer side is reflecting and the inner side is coated or silvered is called a convex mirror. A convex mirror is also referred to as Diverging Mirror as it diverges the light rays after reflection.

Terms related to Spherical Mirrors:

• Pole (P): The center or midpoint of the mirror is called Pole.

• Center of Curvature (C): The geometrical center of the hollow sphere of which the spherical mirror is a part is called the Center of Curvature.

• Principal Axis: The horizontal line passing through the pole and center of curvature is called Principal Axis.

• The radius of Curvature: The radius of the hollow sphere of which the spherical mirror is a part (or) The distance between the Pole of the mirror and the center of curvature is called the Radius of Curvature.

• Focus/Focal Point/Principal Focus (F): The point on the principal axis where all the light rays are incident on the mirror, parallel to the principal axis, converge or appear to come from after reflection.

• Focal Length (f): The distance between the pole of the mirror and the principal focus is known as focal length.

Image: 

The point of convergence or the point from where all the light rays appear to diverge after reflection or refraction is called an Image.

Images are of two types, they are real image and virtual image

Real Image: The image formed when two or more light rays meet at a point after reflection or refraction is known as a Real Image.

Characteristics of Real Image:

• A real image can be caught on screen
• It is always inverted (upside down with respect to the object)
• The size of the real image depends on the position of the object so can be diminished, or of the same size as that of the object, or enlarged
• It is formed by both convex and concave mirrors.

Virtual Image: The image formed when two or more light rays do not actually meet but they appear to meet when produces backward the image is called Virtual Image.

Characteristics of Virtual Image:

• A virtual image cannot be caught on screen
• It is always erect (upside up with respect to the object)
• The size of the virtual image depends on the nature of the mirror
• It is formed by both concave and convex mirrors.

Activity - 1: Finding the normal to a curved surface

Aim: To find the normal to a curved surface

Materials Required: Thin foam or a rubber sole piece, pins

Procedure:

• Take a small piece of thin foam or rubber sole(just like the sole of a slipper).

• Fix small pins along a straight line on the foam as shown in figure 1(a).

• All the pins fixed must be perpendicular to the foam.

• If the foam is considered as the mirror, each pin would represent the normal at that point.

• Any ray incident at the point where pins make contact with the surface will reflect with the same angle as the incident ray made with the pin(normal).

• Now bend the foam piece inwards as depicted in figure 1(b). It appears as a converging mirror. Such mirrors are known as Concave Mirrors. The pins represent the normals at various points.

• Now if we bend the foam piece outwards as depicted in figure 1(c), we can see that pins seem to move away from each other act like a diverging mirror. Such mirrors are known as Convex Mirrors.

• This gives us a clue about how we can find normals to any point on a spherical mirror.

• The only thing is we have to draw a line from the point on the mirror to the center of the sphere.

Result: The line drawn from C to any point on the mirror gives the normal at that point.

Questions related to Activity - 1:

• How the incident ray reflects at the point where the pin makes contact with the surface?

Ans: The incident ray at the point where the pin makes contact with the surface will reflect with the same angle as the incident ray made with the pin-normal.

• If the piece of foam is bent inwards, how it acts?

Ans: If the piece of foam bent inwards, then it acts like a convergent mirror.

• If we bend a piece of foam outwards, what do you observe?

Ans: It is observed that all the pins tend to converge at a point. The bent piece of foam acts like a diverging mirror.

• What do you conclude from the above activity?

Ans: Conclusion:

1. It gives the idea about the nature of spherical mirrors.

2. A rubber sole bent inwards will look like a concave mirror and outwards will appear like a convex mirror.

3. For a concave mirror, all the normals(like pins) will converge towards a point called the center of curvature(C) of the mirror.

4. For the ray R, the incident angle is the angle it makes with the normal (i) and the reflected angle is as 'r'. According to the first law of reflection <i=<r

Activity - 2: Finding the Focus or Focal Point (F) and Focal Length (f) of the spherical mirror: 

Aim: To find the focal point and focal length of a spherical mirror (Concave or Convex).

Materials Required: A plain sheet (paper), concave or convex mirror, object (like sun or candle).

Procedure: 

• Hold a concave mirror perpendicular to the direction of sunlight.
• Take a small piece of paper and slowly moves towards the mirror till the
  
  smallest and the brightest image is obtained on it and observe.

Observation: 

• The rays coming from the sun parallel to the principal axis of a concave mirror converge to a point. This point is called the focus or focal point (F) of the concave mirror.
• Measure the distance of this spot from the pole of the mirror. This distance is called the focal length (f) of the mirror.

Conclusion/Result:

• The point where the image of the sun is formed on the paper sheet is called Focus or Focal Point (F) of the concave mirror.
• The distance measured from the image to the pole of the mirror is called the focal length (f) of the mirror.

Questions related to Activity - 2:

• What happens if you hold the paper at a distance shorter than the focal length from the mirror and move it away?

Ans: It is observed that the image of the sun first keeps on becoming small, then beyond the focal point it keeps on becoming enlarged.

• Does the image of the sun become smaller or bigger?

Ans: At first, the image of the sun is bigger. As we move the paper in front of the mirror, we find the image of the sun become smaller. It is sharp and at the point of focus.

Think and Discuss Questions:

• See figure below. A set of parallel rays are falling on a convex mirror. What conclusions can you draw from this?

Ans: When a set of parallel rays are incident on a convex mirror after reflection they appear to meet at the back of the mirror at a point called Focus (F).

• Will you get a point image if you place a paper at the focal point?

Ans: No, because the rays are actually not converging but appear to meet.

Reflection of Light at plane surface - Part 1

Reflection of Light by Plane Mirror:

Def: The phenomenon of bouncing back of light rays in the same medium when they strike/incident on a smooth flat surface of an object.

Explanation: For mirrors, more than 95% of light may be reflected. Let us understand the concept of reflection from the given side diagram. Reflection of light is like bouncing back of a rubber ball after hitting a wall or any other hard surface.

A Plane Mirror is a flat mirror that is made up of glass and whose backside is coated with a very thin

layer of Silver.

From the side diagram, we can see that a ray PO is striking the polished surface (MM') of the mirror at point O and then bouncing back in the same medium through a ray OQ.

Here PO - Incident Ray, OQ - Reflected Ray, O - Point of Incidence, i - Angle of Incidence, r - Angle of Reflection, Normal - Perpendicular line dividing PO and OQ.

The above concept shows that the reflection of a light ray obeys the following two laws known as Laws of Reflection.

Laws of Reflection: 

The following are the TWO laws of reflection, they are:

1. Angle of Incidence (<i) is equal to angle of reflection (<r) i.e., <i=<r

2. The incident ray, reflected ray and the normal lies in a same plane.

Note: The above two laws of reflection are valid for all types of surfaces including spherical surfaces.

4 Characteristics of plane mirror:

1. The image formed by a plane mirror is virtual, erect and of the same size as that of the object.

2. In a plane mirror, object distance and image distance are same.

3. The size of image and object are equal.

4. The image formed is laterally inverted.

Uses of Plane Mirror:

1. Plane mirror is used as seeing/looking mirror in dressing table to see our own image.

2. It is used in the construction or making of periscope.

3. It is used in automobiles for various uses.

4. It is used in torch light.

5. It is used as shaving mirror.

Fundamentals of Light

What is Light?

Light is a form of energy, which induces the sensation of vision in our eyes and makes us able to see various things present in our surroundings. Under ordinary situations, light travels in a straight line. The straight line followed by light is called Light-ray.

The light ray may be the object's self light (luminous object) or reflected light (non-luminous object).

Luminous Objects: The objects which can emit light on their own. Eg., Sun, Bulb, Tubelight, etc.

Non-Luminous Objects: The objects which cannot emit light on their own. They reflect light from other sources. Eg., Moon, Painting, etc.

7 Most Important Properties of Light:

1. Reflection
2. Refraction
3. Dispersion
4. Scattering
5. Diffraction
6. Interference
7. Polarization

Nature/Characteristics of Light:

• Light is a form of energy

• It is an electromagnetic wave (EM wave)

• It propagates in a straight line

• It is a transverse wave that does not need any medium to travel. It can travel through a vacuum with a speed of 3×10⁸ m/s.

• The velocity of the lightwave changes from one medium to another medium during its propagation.

• The wavelength of light changes from one medium to another medium whereas its frequency remains the same in all the media.

Significance/Importance of Light:

Light may be classified as Natural Light and Artificial Light. In this era, especially human beings cannot imagine their life without light. Light plays an important role in the life all the living creatures present in our planet. 

Importance of Natural Light: Sunlight

• The significance of sunlight could be understand by the photosynthesis process takes place in plants. As plants synthesize nutrients from light and filter the air by consuming carbondioxide and releasing oxygen that we breathe. Hence everything depends on light.

• SunLight plays a key role in maintaining good health. The human being needs to be exposed to sunlight to regulate their body function properly. As we all
  
  
  know that sunlight contains Vitamin D which is necessary to human body.

• The lack of sunlight can cause disturbance in the form of Vitamin D deficiency, Calcium deficiency,  deregulate the release growth harmone. It can also impact the metabolism regulation and also cause fatigue and tiredness.

Importance of Artificial Light:

• Articial light helps in bringing energy to our home even in cloudy and rainy days, at night time.

• Artificial Lighting is very much essential and needful at home to create a pleasant atmosphere that helps to enjoy the life. During occasions light decoration enhances the beauty of that place.

• Now a days, wearing blue light glasses is getting popular as they reduces the risk of eye problems during the usage of smartphones and computers.

The relationship between Physics and Mathematics

The illustration and description of nature begin to be easy if we are free to use Mathematics. We try to get this point by seeing the following example:

To say that Force is equal to the product of the mass of the body and its acceleration, is somewhat lengthy and often difficult to say.

So, by using mathematical terms, we can say it as 

F=ma

Likewise, mathematical techniques such as Trigonometry, calculus, algebra, and geometry can be used to make predictions.

The role of mathematics in physics is to represent the laws in the form of equations and to obtain the conclusion or solutions referring to the observed conditions.

However, Mathematics is the language of physics. Failing to get the knowledge of mathematics leads to face difficulty in discovering, understanding, and explaining the laws of nature. The scope of mathematics in today’s era cannot be argued.

Anyhow, mathematics itself is not physics. We use language to express or convey our message. But the message we want to express has the main focus. If we are poor at the vocabulary and grammar of the language then it would be difficult for us to communicate and express our message.

From the 17^th century, the advancement in the study of mathematics seems to be motivated by the study of physics. A dedicated example of this can be calculus. The creation of calculus

and its enhancement in the concept is strongly related to physics. Newton also regarded Geometry to be a strong branch of Mechanics and the way we see it now; we can be sure that he was right at that time.

As time goes on, more mathematics came into existence and more of them started using physics.

The main goal of physics is to explain the relationship between various measurements of physical objects. A large portion of mathematics is devoted to comprehending and defining the relationships between objects. Therefore, the application of mathematics in physics is undeniable if you consider this aspect common in both subjects.

While learning the subject of physics, the relationship between mathematics and physics must be clearly understood and keep in mind throughout the learning journey of physics.

What is Physics?

When we start studying physics, so many questions raises, the first thing that comes to our mind is what is Physics? Why we study physics? Why physics is so-called a tough subject? What is its implementation in human life? If all the questions are answered properly then we develop an interest in the subject. 

What is Physics?

The word "Physics" is extracted from the Greek word whose meaning is Knowledge of Nature. It is a fundamental science with a wide number of concepts that explain the nature and working secrets of the universe. It explores the accurate description of the material universe. It also deals with matter and energy and their transformations.

Why study Physics?

Physics is a subject of adventurous exploration of universal secrets and their working process. It explains answers and their reasons to our exciting questions such as why the sky is blue, why the body with some mass reaches the ground when we throw it up, why the rainbow occurs, why the rainbow has colors, etc.

Is studying/learning Physics easy?

Studying Physics is challenging, sometimes difficult to understand the concepts but it is often a satisfying subject. Even though Physics gained a reputation as a very difficult subject, yet it is easy and simple if we understand some basic and fundamental laws. If you lodge these laws in your permanent memory then you can easily understand how the whole universe behaves in a variety of situations.

What are the implementations/uses of Physics in our Life?

Physics has an enormous number of applications. It includes:

1.Engineering and Communication

2. Medical Physics

3. Computers

4. Environmental Physics

5. Geophysics

6. Quantum mechanics

7. Theory of relativity                                                       

8. Material Science

It provides an explanation to the questions like why the stars are shining, how the planets revolve around the sun, and so on......