1.0 Nature of Light
Light is a form of energy that produces the sensation of vision. In Class 7, we explore how light behaves when it strikes different surfaces and how it travels through various media. The most fundamental property of light is Rectilinear Propagation—the fact that light travels in straight lines.
Reflection of Light
The phenomenon of "bouncing back" of light into the same medium after striking a polished surface (like a mirror) is called Reflection. It is because of reflection that we can see non-luminous objects around us.
Speed of Light: Approximately $3 \times 10^8\,m/s$ in vacuum or air.
1.1 Laws of Reflection
Reflection is not a random process; it follows two very specific laws that apply to all types of reflecting surfaces (plane or curved):
- The incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane.
- The angle of incidence ($\angle i$) is always equal to the angle of reflection ($\angle r$).
The Law of Reflection
$$\angle i = \angle r$$
Where: $\angle i$ is the angle between incident ray and normal; $\angle r$ is the angle between reflected ray and normal.
Sometimes, the question gives you the angle between the ray and the mirror surface (glancing angle, $g$). Remember, the angle of incidence is measured from the normal.
Formula: $\angle i = 90^\circ - g$
A ray of light strikes a plane mirror such that the angle between the incident ray and the mirror surface is $35^\circ$. Calculate the angle of reflection.
Solution:
1. Given: Angle with mirror surface (glancing angle) = $35^\circ$
2. Find $\angle i$: Since the normal is $90^\circ$ to the surface, $\angle i = 90^\circ - 35^\circ = 55^\circ$.
3. Apply Law: According to the Law of Reflection, $\angle i = \angle r$.
4. Result: $\angle r = 55^\circ$.
Final Answer: The angle of reflection is $55^\circ$.
Light takes only about 8 minutes and 20 seconds to travel the 150 million kilometers from the Sun to the Earth! If the Sun suddenly went out, we wouldn't know for over 8 minutes.
2.0 Image Formation in a Plane Mirror
When we look into a mirror, we see a "copy" of ourselves. In Physics, this is called an Image. The images formed by a plane mirror have distinct characteristics that differentiate them from images formed by lenses or other types of mirrors.
Real vs. Virtual Images
- Real Image: Formed when light rays actually meet at a point. It can be obtained on a screen (e.g., cinema screen).
- Virtual Image: Formed when light rays appear to meet when produced backwards. It cannot be obtained on a screen. Plane mirrors always form virtual images.
2.1 Characteristics of the Image
The image formed by a plane mirror follows these five rules:
- Virtual and Erect: The image is not real and stands upright.
- Same Size: The size of the image is exactly equal to the size of the object.
- Equidistant: The image is as far behind the mirror as the object is in front of it.
- Laterally Inverted: The left side of the object appears as the right side of the image.
2.2 Lateral Inversion
This is a unique phenomenon where the left-right reversal occurs. If you raise your right hand in front of a mirror, your image appears to raise its left hand. This is why the word "AMBULANCE" is written in reverse on the front of the vehicle—so drivers in front can read it correctly in their rearview mirrors.
Object-Image Distance Relation
$$Distance_{Object} = Distance_{Image}$$
Measured perpendicular from the reflecting surface of the mirror.
If a question asks for the distance between the object and its image, you must double the distance from the object to the mirror.
$Total\,Distance = Object\,to\,Mirror + Mirror\,to\,Image$
A boy is standing 3 m in front of a plane mirror. If he moves 1 m towards the mirror, what will be the new distance between the boy and his image?
Solution:
1. Initial Distance: $3\,m$
2. New Object Distance ($u$): He moves $1\,m$ closer, so $3 - 1 = 2\,m$.
3. New Image Distance ($v$): In a plane mirror, $u = v$, so image is also $2\,m$ behind.
4. Total Distance: $u + v = 2\,m + 2\,m = 4\,m$.
Final Answer: The distance between the boy and his image is $4\,m$.
A Periscope uses two plane mirrors placed at a $45^\circ$ angle to allow a person to see over obstacles or from inside a submarine! It relies on the principle of double reflection.
3.0 Multiple Reflections
When an object is placed between two mirrors inclined at an angle, the image formed by one mirror acts as an object for the second mirror. This leads to the formation of multiple images. The number of images depends entirely on the angle between the two mirrors.
Number of Images Formula
$$n = \left(\frac{360^\circ}{\theta}\right) - 1$$
Where: $n$ = number of images, $\theta$ = angle between the mirrors (in degrees).
3.1 Special Cases of Inclination
- Parallel Mirrors ($\theta = 0^\circ$): If two mirrors are placed parallel to each other, an infinite number of images are formed (as seen in barber shops).
- Perpendicular Mirrors ($\theta = 90^\circ$): The number of images formed is $n = (360/90) - 1 = 3$.
3.2 The Kaleidoscope
A Kaleidoscope is an optical instrument that works on the principle of multiple reflections. It usually consists of three plane mirrors inclined at an angle of 60° to each other, forming an equilateral triangle. As the tube is rotated, the colourful glass pieces inside create beautiful, symmetrical, and ever-changing patterns.
If the value of $\frac{360}{\theta}$ is an odd integer and the object is placed asymmetrically, the number of images is simply $\frac{360}{\theta}$. However, for Class 7 ICSE, we generally follow the formula $n = (\frac{360}{\theta}) - 1$ for all even symmetric cases.
How many images will be formed if an object is placed between two plane mirrors inclined at an angle of 72°?
Solution:
1. Given Angle ($\theta$): $72^\circ$
2. Formula: $n = (\frac{360}{\theta}) - 1$
3. Calculation: $n = (\frac{360}{72}) - 1 = 5 - 1 = 4$.
Final Answer: 4 images will be formed.
The Kaleidoscope was invented by the Scottish physicist Sir David Brewster in 1816. He originally intended it as a scientific tool, but it quickly became a popular toy worldwide!
4.0 Speed of Image in a Plane Mirror
A fascinating aspect of reflection is how the image responds when the object or the mirror moves. This is a common topic for competitive exams and higher-order thinking questions in ICSE Physics.
4.1 When the Object Moves
If an object moves toward or away from a fixed mirror with a speed $v$, the image also moves toward or away from the mirror with the same speed $v$. However, the speed of the image relative to the object is doubled.
Relative Speed Formula
$$V_{relative} = 2 \times V_{object}$$
This is because both object and image are moving toward each other.
5.0 Spherical Mirrors: An Introduction
Not all mirrors are flat. Mirrors that have curved reflecting surfaces are called Spherical Mirrors. They are considered parts of a hollow glass sphere.
- Concave Mirror: The reflecting surface is curved inwards (like the inner surface of a spoon). It is also called a Converging Mirror.
- Convex Mirror: The reflecting surface is curved outwards (like the back of a spoon). It is also called a Diverging Mirror.
A simple way to remember: "Cave" goes in. So, a Concave mirror is the one where the reflecting surface is like a cave entry.
A girl runs towards a plane mirror at a speed of 2 m/s. At what speed does her image approach her?
Solution:
1. Speed of object ($V_o$): $2\,m/s$
2. Speed of image ($V_i$): The image also moves at $2\,m/s$ toward the mirror.
3. Relative Speed: Since they move toward each other, $V_{rel} = V_o + V_i = 2 + 2 = 4\,m/s$.
Final Answer: Her image approaches her at a speed of $4\,m/s$.
The rear-view mirrors in cars are usually Convex mirrors. This is because they provide a wider field of view, helping drivers see more traffic behind them, although objects appear smaller than they really are.
6.0 Colours and the Spectrum
White light, such as sunlight, appears to be a single colour, but it is actually a mixture of seven different colours. This was first demonstrated by Sir Isaac Newton using a glass prism.
6.1 Dispersion of Light
The phenomenon of splitting white light into its constituent colours when it passes through a transparent medium (like a prism) is called Dispersion. The band of seven colours obtained is called the Spectrum.
The colours are remembered by the acronym VIBGYOR:
- Violet, Indigo, Blue, Green, Yellow, Orange, and Red.
6.2 Primary and Secondary Colours
In Physics, we categorize colours based on how they combine to form other colours. This is known as Colour Addition.
Types of Colours
- Primary Colours: These are Red, Green, and Blue (RGB). They cannot be obtained by mixing other colours. Combining all three in equal proportions gives White light.
- Secondary Colours: These are formed by mixing two primary colours.
- Red + Green = Yellow
- Red + Blue = Magenta
- Blue + Green = Cyan
Complementary Colours
Blue + Yellow = White
Green + Magenta = White
Red + Cyan = White
Any two colours that combine to produce white light are called Complementary Colours.
Primary colours of Light (Red, Green, Blue) are different from primary colours of Paints/Pigments (Red, Yellow, Blue). Mixing all primary light colours creates White, but mixing all primary paint colours creates Black!
A red rose is seen in green light. What colour will it appear to be?
Solution:
1. An object appears red because it reflects only red light and absorbs all other colours.
2. When green light falls on the red rose, there is no red component to be reflected.
3. The green light is absorbed by the rose.
Final Answer: The rose will appear Black.
A Rainbow is a natural spectrum caused by the dispersion of sunlight by tiny water droplets in the atmosphere, which act like millions of tiny prisms!