1.0 Nature and Reflection of Light
Light is a form of energy which produces the sensation of vision. When light falls on a surface, it may be absorbed, transmitted, or bounced back. The phenomenon of return of light into the same medium after striking a surface is called Reflection of Light.
Terminology of Reflection
- Incident Ray: The light ray striking the reflecting surface.
- Reflected Ray: The light ray which bounces back from the surface.
- Normal: The perpendicular line drawn at the point of incidence.
- Angle of Incidence ($i$): Angle between the incident ray and the normal.
- Angle of Reflection ($r$): Angle between the reflected ray and the normal.
1.1 Laws of Reflection
Reflection of light follows two fundamental laws, whether the surface is smooth (Regular Reflection) or rough (Diffused Reflection):
- The incident ray, the reflected ray, and the normal at the point of incidence, all lie in the same plane.
- The angle of incidence is always equal to the angle of reflection ($i = r$).
Angle of Deviation ($\delta$)
The angle through which a ray of light is turned from its original path:
$$\delta = 180^\circ - (i + r) = 180^\circ - 2i$$
1.2 Reflection at Plane Mirrors
A plane mirror forms an image with the following characteristics:
- Virtual and Erect: The image cannot be caught on a screen.
- Same Size: Size of image = Size of object.
- Same Distance: Object distance ($u$) = Image distance ($v$).
- Laterally Inverted: The left of the object appears as the right of the image.
If a ray of light falls normally on a mirror (perpendicular to the surface), the angle of incidence ($i$) is $0^\circ$. Therefore, the angle of reflection ($r$) is also $0^\circ$, and the ray retraces its path.
A ray of light is incident on a plane mirror such that the angle between the incident ray and the mirror surface is 35°. Calculate the angle of reflection.
Solution:
1. Glancing Angle: $35^\circ$ (Angle with the surface).
2. Angle of Incidence ($i$): Normal is $90^\circ$ to surface. So, $i = 90^\circ - 35^\circ = \mathbf{55^\circ}$.
3. Law of Reflection: $r = i$.
Final Answer: The angle of reflection is $55^\circ$.
Why is the word AMBULANCE written laterally inverted on the front of the vehicle? It’s because of Lateral Inversion! Drivers in front see the correct spelling in their rearview mirrors and can immediately give way.
2.0 Images Formed by Two Plane Mirrors
When an object is placed between two plane mirrors inclined at an angle, multiple images are formed. This is because the image formed by one mirror acts as a virtual object for the second mirror. This process continues until the final image falls behind the reflecting surfaces.
Number of Images Formula
If $\theta$ is the angle between two mirrors, let $n = \frac{360^\circ}{\theta}$:
2. If $n$ is Odd (Object placed symmetrically): $N = n - 1$
3. If $n$ is Odd (Object placed asymmetrically): $N = n$
2.1 Parallel and Perpendicular Mirrors
The number of images changes drastically based on how the mirrors are positioned:
- Parallel Mirrors ($\theta = 0^\circ$): An infinite number of images are formed (seen in barber shops). However, the images become dimmer as they get farther away due to light absorption.
- Perpendicular Mirrors ($\theta = 90^\circ$): Here $n = 360/90 = 4$. Since 4 is even, $N = 4 - 1 = \mathbf{3}$ images.
2.2 Optical Instruments
Multiple reflection is used in various optical toys and instruments:
- Kaleidoscope: Uses three plane mirrors inclined at $60^\circ$ to form beautiful symmetrical patterns using colored glass pieces.
- Periscope: Uses two plane mirrors placed parallel to each other and inclined at $45^\circ$ to the path of light. It allows an observer to see objects over an obstacle or from a submarine.
If the calculation for $n = \frac{360}{\theta}$ results in a fraction (e.g., 3.6), the number of images is taken as the integral part (e.g., 3). Always check if the value is even or odd before subtracting 1!
Two plane mirrors are inclined at an angle of 72°. How many images will be formed of an object placed symmetrically between them?
Solution:
1. Step 1: Calculate $n = \frac{360^\circ}{\theta} = \frac{360}{72} = 5$.
2. Step 2: 5 is an odd number.
3. Step 3: Since the object is placed symmetrically, we use the formula $N = n - 1$.
4. Calculation: $N = 5 - 1 = \mathbf{4}$.
Final Answer: 4 images will be formed.
The Periscope was widely used in the trenches of World War I, allowing soldiers to see over the edge of the trench without exposing themselves to enemy fire. Modern submarines use high-tech digital versions, but the basic physics remains the same!
3.0 Spherical Mirrors
A Spherical Mirror is a mirror whose reflecting surface is a part of a hollow sphere of glass. Depending on which side is polished and which side is reflecting, spherical mirrors are classified into two types: Concave and Convex.
Types of Spherical Mirrors
- Concave Mirror: The reflecting surface is curved inwards (like the inside of a spoon). It is also called a Converging Mirror because it brings parallel rays to a single point.
- Convex Mirror: The reflecting surface is curved outwards (like the back of a spoon). It is also called a Diverging Mirror because it spreads out parallel rays.
3.1 Important Terms Related to Spherical Mirrors
To draw ray diagrams, you must be familiar with the following geometric centers and lines:
- Center of Curvature (C): The center of the hollow sphere of which the mirror is a part.
- Pole (P): The geometric center of the reflecting spherical surface.
- Principal Axis: The straight line passing through the Pole and the Center of Curvature.
- Radius of Curvature (R): The distance between the Pole and the Center of Curvature ($PC$).
- Principal Focus (F): The point on the principal axis where rays parallel to the axis meet (or appear to meet) after reflection.
Relation between f and R
For mirrors of small aperture, the focal length is exactly half of the radius of curvature:
$$f = \frac{R}{2}$$
1. A Concave Mirror has a Real Focus because light rays actually meet there. It is in front of the mirror.
2. A Convex Mirror has a Virtual Focus because light rays only appear to meet there when produced backward. It is behind the mirror.
The radius of curvature of a convex mirror used as a rear-view mirror in a car is 3.0 m. Find its focal length.
Solution:
1. Given: Radius of Curvature ($R$) = $3.0\,m$.
2. Formula: $f = R / 2$.
3. Calculation: $f = 3.0 / 2 = \mathbf{1.5\,m}$.
Final Answer: The focal length of the mirror is $1.5\,m$.
A Concave Mirror is used by dentists to see a larger image of your teeth. When the object is very close to the mirror (between P and F), it produces a magnified, virtual, and erect image!
4.0 Rules for Drawing Ray Diagrams
To determine the position, size, and nature of the image formed by a spherical mirror, we use Ray Diagrams. While countless rays travel from an object, we only need to trace any two of the following four principal rays to find the point of intersection (the image).
The Four Standard Rays
- Parallel Ray: A ray parallel to the principal axis, after reflection, passes through the Focus (F) of a concave mirror or appears to diverge from it in a convex mirror.
- Focus Ray: A ray passing through (or directed towards) the Focus (F) becomes parallel to the principal axis after reflection.
- Center of Curvature Ray: A ray passing through C strikes the mirror normally and retraces its path back through C.
- Pole Ray: A ray incident at the Pole (P) is reflected such that the angle of incidence equals the angle of reflection ($i = r$).
4.1 Image Formation by Concave Mirror
The nature of the image formed by a concave mirror changes based on the object's distance from the pole. Here are the most important cases for your exams:
| Object Position | Image Position | Nature & Size |
|---|---|---|
| At Infinity | At Focus (F) | Real, Inverted, Highly Diminished. |
| At C | At C | Real, Inverted, Same Size. |
| Between F and P | Behind Mirror | Virtual, Erect, Magnified. |
Mirror Formula & Magnification
$$\frac{1}{f} = \frac{1}{v} + \frac{1}{u} \quad | \quad m = \frac{h_i}{h_o} = -\frac{v}{u}$$
Where: $u$ = object distance, $v$ = image distance, $f$ = focal length.
1. All distances are measured from the Pole (P).
2. Distances in direction of incident light are Positive.
3. Distances against incident light are Negative.
Pro Tip: $u$ is always negative. For a concave mirror, $f$ is negative. For a convex mirror, $f$ is positive.
An object is placed 20 cm in front of a concave mirror of focal length 15 cm. Find the position of the image.
Solution:
1. Given: $u = -20\,cm$ (always negative), $f = -15\,cm$ (concave mirror).
2. Mirror Formula: $\frac{1}{v} = \frac{1}{f} - \frac{1}{u}$
3. Calculation: $\frac{1}{v} = \frac{1}{-15} - \frac{1}{-20} = -\frac{1}{15} + \frac{1}{20}$
4. $\frac{1}{v} = \frac{-4 + 3}{60} = -\frac{1}{60} \Rightarrow \mathbf{v = -60\,cm}$.
Final Answer: The image is formed at a distance of $60\,cm$ in front of the mirror (Real image).
A Convex Mirror is always used as a rear-view mirror because it always produces a diminished, erect, and virtual image. This provides a much wider field of view compared to a plane mirror, allowing drivers to see more traffic behind them!
5.0 Practical Applications of Spherical Mirrors
The unique ways in which concave and convex mirrors reflect light makes them indispensable in modern technology. Their utility is primarily determined by their ability to either converge light to a point or diverge it to cover a wide area.
5.1 Uses of Concave Mirrors
Concave mirrors are used wherever we need to concentrate light or see a magnified view of a nearby object:
- Shaving/Makeup Mirrors: When the face is held between the Pole and Focus, a magnified and erect image is seen.
- Doctor's Head Mirrors: Used by ENT specialists to reflect a beam of light into small areas like the ear or throat.
- Searchlights and Torches: The bulb is placed at the Focus. The light rays strike the mirror and emerge as a powerful, parallel beam.
- Solar Furnaces: Large concave mirrors converge sunlight to a focal point, producing intense heat for melting metals or generating power.
5.2 Uses of Convex Mirrors
Convex mirrors are preferred when a wide field of view is required:
- Rear-View Mirrors: They always form an erect, though diminished, image. This allows drivers to monitor a much larger area of traffic than a plane mirror would allow.
- Security Mirrors in Shops: A single large convex mirror placed in a corner allows a shopkeeper to observe multiple aisles at once.
- Blind Turns: Placed at sharp "hairpin" bends on roads to help drivers see oncoming traffic from the other side.
Power of a Mirror (Conceptual)
While lenses are usually measured by power, mirrors are defined by their ability to converge/diverge:
Converging Power $\propto \frac{1}{f}$
Shorter the focal length, stronger the convergence or divergence.
Have you noticed this warning on car side mirrors? Because convex mirrors diminish the size of the image, our brain perceives the object to be farther away than it actually is. Always use caution when changing lanes!
A convex mirror has a radius of curvature of 20 cm. If an object is placed 10 cm from the mirror, calculate the magnification produced.
Solution:
1. Given: $R = +20\,cm \Rightarrow f = R/2 = +10\,cm$. Object distance $u = -10\,cm$.
2. Find $v$: $\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{10} - \frac{1}{-10} = \frac{1}{10} + \frac{1}{10} = \frac{2}{10}$.
3. So, $v = +5\,cm$ (Image is behind the mirror).
4. Magnification ($m$): $m = -v/u = -(5)/(-10) = \mathbf{+0.5}$.
Final Answer: The magnification is 0.5. The image is half the size of the object and erect.
The Hubble Space Telescope uses a massive concave mirror (2.4 meters wide) to collect light from distant galaxies. Because there is no atmosphere in space to distort the light, it can see objects billions of light-years away!