Hello, and welcome to today's lesson on Light Energy. I'm excited to guide you through this fascinating chapter where we explore how light behaves when it travels through different materials, and how mirrors can create images of the world around us. Today, we will learn about refraction, spherical mirrors, and the beautiful phenomenon of dispersion that splits white light into rainbow colours.
Let us begin by understanding how fast light travels. Light moves at an incredible speed of 3 × 10⁸ m/s in air or vacuum. However, when light enters water, its speed drops to 2.25 × 10⁸ m/s. In glass, it slows down even further to 2 × 10⁸ m/s.
Now, here is an important idea. When light slows down in a material, we call that material optically denser. So glass is optically denser than water, and water is optically denser than air. Conversely, air is optically rarer than both water and glass. The slower the light moves in a medium, the denser that medium is considered to be.
Let us now explore what happens when light crosses from one medium to another. Imagine you are looking at a coin at the bottom of a water-filled vessel. The coin appears closer to the surface than it actually is. This happens because light changes direction when it moves from water to air. This bending of light is called refraction.
Refraction is defined as the change in direction of path of light when it passes from one optically transparent medium to another.
Here are three key observations about refraction. First, when light travels from a rarer medium to a denser medium, such as from air into water or glass, it bends towards the normal. Second, when light travels from a denser medium to a rarer medium, such as from water into air, it bends away from the normal. Third, when light falls normally, that is, perpendicular to the surface, it passes straight through without any bending.
Let me explain some important terms. The incident ray is the light ray that strikes the boundary between two media. The refracted ray is the light ray that travels in the second medium after bending. The normal is an imaginary line drawn perpendicular to the surface at the point where the incident ray strikes. The angle of incidence, denoted by i, is the angle between the incident ray and the normal. The angle of refraction, denoted by r, is the angle between the refracted ray and the normal.
Now we come to the laws that govern refraction, known as Snell's laws.
First law: the incident ray, the normal at the point of incidence, and the refracted ray all lie in the same plane. Second law: for a given pair of media and for light of a given colour, the ratio of the sine of angle of incidence to the sine of angle of refraction is constant. This constant is called the refractive index, represented by the Greek letter μ.
Mathematically, we write this as: μ = sin i / sin r. The refractive index can also be expressed as the ratio of the speed of light in the first medium to the speed of light in the second medium. Or μ = v₁/v₂, where v₁ is the speed in the first medium and v₂ is the speed in the second medium. For example, the refractive index of water with respect to air is 4/3, or approximately 1.33. The refractive index of glass with respect to air is 1.5. Remember, air has a refractive index of 1, and no medium can have a refractive index less than 1.
Refraction creates several interesting effects in our daily life. When you look at the bottom of a water-filled pond from above, the water appears shallower than it really is. This is because light rays from the bottom bend away from the normal as they leave the water and enter the air. Your eye traces these rays back in a straight line, making the bottom appear raised. The apparent depth is about three-fourths of the real depth.
Have you ever noticed a mirage on a hot desert road? This too is caused by refraction. The hot sand heats the air near the ground, making it rarer than the cooler air above. Light from distant objects bends as it passes through these layers of different densities, creating an inverted image that looks like water.
Even sunrise and sunset are affected by refraction. The atmosphere bends sunlight towards the earth when the sun is actually below the horizon. This makes the sun appear to rise a few minutes early and set a few minutes late.
Now let us explore what happens when light passes through a glass block or a prism. When light enters a rectangular glass block, it bends towards the normal at the first surface. Inside the glass, it travels in a straight line. When it exits at the opposite parallel surface, it bends away from the normal. The emergent ray is parallel to the incident ray but is shifted sideways. This sideways shift is called lateral displacement.
A prism is different. It has two inclined surfaces that are not parallel to each other. When light passes through a prism, it bends towards the base of the prism at both surfaces. Unlike the glass block, the emergent ray is not parallel to the incident ray.
Here comes one of the most beautiful phenomena in optics: dispersion. When white light passes through a prism, it splits into seven colours. This band of colours is called the spectrum. The order of colours from the base of the prism upwards is violet, indigo, blue, green, yellow, orange, and red. You can remember this order using the word VIBGYOR.
Dispersion is defined as the splitting of white light into its constituent colours when passed through a prism.
Why does this happen? Different colours of light travel at different speeds in glass or water. Violet light travels slowest and bends the most toward the base. Red light travels fastest and bends the least toward the base. Since each colour has a slightly different refractive index, they separate and spread out into a spectrum. The prism does not create these colours; it merely separates the colours that already exist in white light.
This same principle creates rainbows in the sky. After rain, water droplets in the air act like tiny prisms, dispersing sunlight into beautiful arcs of colour.
Now we turn our attention to mirrors, specifically spherical mirrors. A spherical mirror is made by silvering a part of a hollow glass sphere. There are two types: concave mirrors and convex mirrors.
A concave mirror is made by silvering the outer surface of a hollow sphere so that reflection takes place from the inner hollow surface. A convex mirror is made by silvering the inner surface such that reflection takes place from the outer convexed surface.
Let me introduce the key terms used with spherical mirrors. The pole is the geometric centre of the mirror's surface. The centre of curvature is the centre of the sphere from which the mirror was made. The radius of curvature is the distance from the centre of curvature to any point on the mirror surface. The principal axis is the straight line joining the pole to the centre of curvature.
Now, what happens when parallel rays of light strike a spherical mirror? In a concave mirror, parallel rays converge at a point on the principal axis after reflection. This point is called the focus of the concave mirror. In a convex mirror, parallel rays appear to diverge from a point behind the mirror. This point is the virtual focus of the convex mirror.
The focal length is the distance from the pole to the focus.
There is a simple relationship: focal length equals half the radius of curvature. In formula form, f = R/2, or R = 2f.
To draw ray diagrams for spherical mirrors, we use three special rays. First, a ray passing through the centre of curvature strikes the mirror normally and reflects back along the same path. Second, a ray parallel to the principal axis reflects through the focus in a concave mirror, or appears to come from the focus in a convex mirror. Third, a ray passing through the focus reflects parallel to the principal axis. Any two of these rays help us locate where the image forms.
Images formed by mirrors can be real or virtual. A real image is formed when the reflected rays actually meet at a point. It can be projected on a screen and is always inverted. A virtual image is formed when the reflected rays appear to meet at a point when produced backwards. It cannot be obtained on a screen and is erect or upright.
For a concave mirror, the nature of the image depends on where the object is placed. If the object is beyond the centre of curvature, the image forms between the focus and centre of curvature. It is real, inverted, and smaller than the object. When the object is at the centre of curvature, the image forms at the same position. It is real, inverted, and the same size as the object. When the object is between the centre of curvature and focus, the image forms beyond the centre of curvature. It is real, inverted, and larger than the object.
When the object is exactly at the focus, the reflected rays become parallel. The image forms at infinity. It is real, inverted, and highly magnified. But here is something interesting. When the object is placed between the focus and the pole, the image forms behind the mirror. It is virtual, erect, and enlarged. This is why concave mirrors make excellent shaving mirrors.
For a convex mirror, the situation is simpler. No matter where the object is placed, the image is always virtual, erect, and smaller than the object. The image always forms between the pole and the focus, behind the mirror. As the object moves closer to the mirror, the image also moves closer and becomes slightly larger, though still diminished.
Let us consider some practical applications. Concave mirrors are used as shaving mirrors because they produce enlarged virtual images when the face is close. They serve as reflectors in torches and searchlights, where placing the bulb at the focus produces a parallel beam of light. Doctors use concave mirrors as head mirrors to concentrate light on small areas to be examined, like nose, throat, ear, or teeth. Solar cookers use concave mirrors to converge sun-rays on the cooking material placed at the focus.
Convex mirrors are widely used as rear-view mirrors in vehicles. They provide a wider field of view than a plane mirror, enabling a driver to see all the traffic behind. They are also used as reflectors in street lamps to diverge light over a large area, and as vigilance or anti-theft mirrors in big showrooms and departmental stores.
Let us recap the key points from today's lesson. First, refraction is the bending of light when it passes from one transparent medium to another. Light bends towards the normal when going from rarer to denser medium, and away from the normal when going from denser to rarer medium.
Second, the refractive index measures how much a medium bends light, and it equals the ratio of light's speed in the first medium to its speed in the second medium.
Third, dispersion is the splitting of white light into seven colours by a prism, forming a spectrum in the order VIBGYOR.
Fourth, spherical mirrors are of two types: concave mirrors that converge light and convex mirrors that diverge light.
Fifth, the focal length of a spherical mirror equals half its radius of curvature.
Sixth, concave mirrors can form both real and virtual images depending on object position, while convex mirrors always form virtual, erect, and diminished images.
Light energy surrounds us constantly, from the colours we see to the reflections in mirrors. Understanding how light behaves helps us appreciate the beauty of rainbows and the technology behind telescopes and microscopes. Keep observing the world of light around you, and remember, physics is not just in textbooks, it is everywhere in nature. Thank you for listening, and I look forward to our next exploration together.