1.0 Refraction of Light
In previous classes, we studied how light bounces off surfaces (Reflection). In Class 8, we explore what happens when light travels from one transparent medium to another. This bending of light as it passes obliquely from one medium to another is called Refraction.
Why does Light Bend?
The fundamental cause of refraction is the change in the speed of light when it enters a different medium. Light travels fastest in a vacuum ($3 \times 10^8\,m/s$) and slows down in denser media like water or glass.
- Optical Rarer Medium: A medium in which the speed of light is more (e.g., Air).
- Optical Denser Medium: A medium in which the speed of light is less (e.g., Glass).
1.1 Laws of Refraction
Refraction is governed by two primary laws:
- The incident ray, the refracted ray, and the normal at the point of incidence, all lie in the same plane.
- Snell's Law: For a given pair of media, the ratio of the sine of the angle of incidence ($i$) to the sine of the angle of refraction ($r$) is constant.
Refractive Index ($\mu$)
$$\mu = \frac{\sin i}{\sin r} = \frac{c}{v}$$
Where: $c$ = speed of light in vacuum, $v$ = speed of light in medium.
1. When light travels from Rarer to Denser: It bends towards the normal ($i > r$).
2. When light travels from Denser to Rarer: It bends away from the normal ($i < r$).
3. If light strikes normally ($i = 0^\circ$): It passes undeviated.
The speed of light in a transparent medium is $2 \times 10^8\,m/s$. Calculate the refractive index of the medium.
Solution:
1. Speed in vacuum ($c$): $3 \times 10^8\,m/s$
2. Speed in medium ($v$): $2 \times 10^8\,m/s$
3. Formula: $\mu = c / v$
4. Calculation: $\mu = \frac{3 \times 10^8}{2 \times 10^8} = 1.5$
Final Answer: The refractive index of the medium is $1.5$ (Note: It has no unit).
A swimming pool always appears shallower than it actually is due to refraction. The light from the bottom bends away from the normal as it enters the air, making the floor look shifted upwards!
2.0 Refraction through a Prism
A Prism is a transparent refracting medium bounded by five plane surfaces, with two opposite triangular faces and three rectangular lateral surfaces. When light passes through a prism, it doesn't just bend; it undergoes a specific change in direction called Deviation.
2.1 Angle of Deviation
When a ray of light enters a prism, it bends towards the normal at the first surface and away from the normal at the second surface. The total angle through which the incident ray is turned is called the Angle of Deviation ($\delta$).
The Prism Relation
$$i + e = A + \delta$$
Where: $i$ = angle of incidence, $e$ = angle of emergence, $A$ = angle of prism, $\delta$ = angle of deviation.
2.2 Dispersion of White Light
In 1666, Sir Isaac Newton discovered that when white light (like sunlight) passes through a prism, it splits into a beautiful band of seven colours. This phenomenon is called Dispersion.
The Spectrum (VIBGYOR)
The band of colours obtained on a screen after dispersion is called a Spectrum. The colours appear in the order: Violet, Indigo, Blue, Green, Yellow, Orange, and Red.
- Red light: Deviates the least (highest wavelength).
- Violet light: Deviates the most (lowest wavelength).
White light is a mixture of seven colours. Dispersion occurs because each colour of light has a different speed in a glass prism. Therefore, each colour bends through a different angle of deviation, causing them to spread out.
In a prism of angle 60°, the angle of incidence is 45° and the angle of emergence is 40°. Calculate the angle of deviation.
Solution:
1. Given: $A = 60^\circ, i = 45^\circ, e = 40^\circ$.
2. Formula: $i + e = A + \delta$
3. Rearranging: $\delta = (i + e) - A$
4. Calculation: $\delta = (45 + 40) - 60 = 85 - 60 = 25^\circ$.
Final Answer: The angle of deviation is $25^\circ$.
A Rainbow is a natural spectrum appearing in the sky. It is caused by the dispersion of sunlight as it passes through tiny water droplets in the atmosphere, which act like millions of tiny prisms!
3.0 Spherical Lenses
A lens is a piece of transparent refracting material (usually glass) bound by two spherical surfaces or one spherical and one plane surface. Lenses work on the principle of refraction to converge or diverge light rays to form images.
3.1 Types of Lenses
There are two primary types of spherical lenses that we study in the ICSE curriculum:
- Convex Lens (Converging): Thicker in the middle and thinner at the edges. It converges parallel rays of light to a single point.
- Concave Lens (Diverging): Thinner in the middle and thicker at the edges. It diverges parallel rays of light, making them appear to come from a single point.
3.2 Important Terms Related to Lenses
To master ray diagrams, you must be familiar with these technical terms:
- Optical Centre ($O$): The geometric centre of the lens. A ray passing through $O$ goes undeviated.
- Principal Axis: An imaginary straight line passing through the centres of curvature of the two surfaces of the lens.
- Principal Focus ($F$): The point on the principal axis where rays parallel to the axis meet (Convex) or appear to diverge from (Concave).
- Focal Length ($f$): The distance between the Optical Centre and the Principal Focus.
Lens Power Formula
$$P = \frac{1}{f}$$
Where: $P$ = Power in Dioptres (D), $f$ = Focal length in metres.
1. The focal length of a Convex lens is always taken as Positive (+).
2. The focal length of a Concave lens is always taken as Negative (-).
Always convert focal length to metres before calculating the power in Dioptres.
A convex lens has a focal length of 20 cm. Calculate its power.
Solution:
1. Focal length ($f$): $20\,cm = 0.2\,m$.
2. Type: Convex (so $f$ is positive).
3. Formula: $P = 1 / f$.
4. Calculation: $P = 1 / 0.2 = +5\,D$.
Final Answer: The power of the lens is $+5\,Dioptres$.
The crystalline lens inside the human eye is a natural convex lens. It can change its shape to adjust its focal length, allowing you to see objects clearly at different distances!
4.0 Image Formation by a Convex Lens
A convex lens can form images of various sizes and natures depending on the distance of the object from the optical centre. To understand these, we use Ray Diagrams based on three standard rules:
- A ray parallel to the principal axis passes through the Focus ($F$) after refraction.
- A ray passing through the Optical Centre ($O$) goes undeviated.
- A ray passing through the Focus ($F$) becomes parallel to the principal axis after refraction.
4.1 Standard Object Positions
The characteristics of the image change as the object moves closer to the lens:
| Object Position | Image Position | Nature & Size |
|---|---|---|
| At Infinity | At Focus ($F$) | Real, Inverted, Point-sized |
| Beyond $2F$ | Between $F$ and $2F$ | Real, Inverted, Diminished |
| At $2F$ | At $2F$ | Real, Inverted, Same size |
| Between $F$ and $O$ | Behind the object | Virtual, Erect, Magnified |
Linear Magnification ($m$)
$$m = \frac{h_i}{h_o} = \frac{v}{u}$$
Where: $h_i$ = height of image, $h_o$ = height of object, $v$ = image distance, $u$ = object distance.
A Real Image is always inverted and can be obtained on a screen (formed by actual intersection of rays). A Virtual Image is always erect and cannot be caught on a screen. A convex lens is unique because it can form both types!
An object of height 5 cm is placed at a distance of 10 cm from a convex lens. If the image is formed at 20 cm on the other side, find the magnification and the height of the image.
Solution:
1. Given: $h_o = 5\,cm, u = -10\,cm$ (object is left), $v = +20\,cm$ (real image is right).
2. Magnification ($m$): $v / u = 20 / (-10) = -2$.
3. Image Height ($h_i$): $m \times h_o = (-2) \times 5 = -10\,cm$.
Final Answer: Magnification is $2$ (inverted), and image height is $10\,cm$.
A Magnifying Glass is simply a convex lens where the object is placed very close (between $F$ and $O$). This creates the large, upright virtual image that helps you read tiny text!
5.0 The Human Eye and Vision
The human eye is nature’s most sophisticated optical instrument. It works remarkably like a camera, using a crystalline convex lens to form real and inverted images of objects on a light-sensitive screen called the Retina.
Power of Accommodation
The ability of the eye lens to adjust its focal length to see both nearby and distant objects clearly is called Accommodation. This is achieved by the Ciliary Muscles which change the curvature of the lens.
- Far Point: The maximum distance up to which the eye can see clearly (Infinity for a normal eye).
- Near Point: The minimum distance for clear vision without strain (25 cm for a normal adult eye).
5.1 Common Defects of Vision
When the eye loses its power of accommodation or the eyeball changes shape, images do not form correctly on the retina. These are corrected using external lenses:
| Defect | Description | Correction |
|---|---|---|
| Myopia (Short-sightedness) | Can see nearby objects but not distant ones. Image forms in front of retina. | Concave Lens |
| Hypermetropia (Long-sightedness) | Can see distant objects but not nearby ones. Image forms behind the retina. | Convex Lens |
Persistence of Vision
Duration = 1/16th of a second
The impression of an image stays on the retina for a short time. If images flash faster than this, they appear to be in continuous motion (the principle behind cinema).
Don't confuse Hypermetropia with Presbyopia. While both make nearby vision difficult, Presbyopia occurs specifically due to aging as ciliary muscles weaken. It is often corrected with Bifocal Lenses.
A person is prescribed a lens of power -2.5 D. What defect of vision does he have, and what is the focal length of the lens?
Solution:
1. Sign of Power: The power is negative ($-2.5\,D$).
2. Defect: Since only a Concave lens has negative power, the person suffers from Myopia.
3. Focal Length ($f$): $f = 1 / P = 1 / (-2.5) = -0.4\,m$.
4. In cm: $-0.4 \times 100 = -40\,cm$.
Final Answer: The person has Myopia; Focal length is $40\,cm$ (concave).
The Blind Spot is a small area on the retina where the optic nerve leaves the eye. It has no light-sensitive cells (rods or cones), so no image can be seen if it falls on this spot!