Light and Optics

Spherical lens

What is a spherical lens? We have previously learned about spherical mirrors. We learned that the reflecting surface of a spherical mirror was part of a sphere. Similarly, the refracting surface of a spherical lens is part of a sphere. You will note that here we have used the word refracting rather than reflecting. Thus, a lens causes refraction of light.

A spherical lens is of two types- convex and concave.

A convex spherical lens is thicker at the centre and thinner at the edges. Light rays converge on entering a convex lens thus earning the name-converging lens.

A concave spherical lens is thicker at the edges and thinner at the centre. Light rays diverge from a concave lens, hence the name diverging lens.

There are a few terms that one should know about when studying spherical lens.

Optical centre: The central point of the lens

Centre of curvature: Previously, we have learned about the centre of curvature of spherical mirrors. A similar concept works in a spherical lens as well. Each surface of the lens is a part of a sphere. The centre of each sphere is the centre of curvature of the surface of the lens. As a spherical lens has two refracting surfaces, each lens has two centre of curvature- C1 and C2.

Principal Axis of the lens: A line drawn through the centre of curvatures of the spherical lens.

Principal focus (convex lens): A point on the principal axis where light rays parallel to the principal axis converge after passing through the lens.

Principal focus (concave lens): A point on the principal axis from where light rays (initially parallel to the principal axis) appear to diverge after passing through the lens.

Focal length (f): The distance between the principal focus and the optical centre.

Laws of refraction through a spherical lens

  1. A ray of light parallel to the principal axis after refraction passes through the principal focus on the other side of a convex lens or appears to diverge from the principal focus on the same side of a concave lens.
  2. A ray appearing to meet at the principal focus of a concave lens or passing through the principal focus of a convex lens, after refraction emerges parallel to the principal axis.
  3. A ray passing through the optical centre of a concave of or convex lens does not deviate.

Characteristics of image formed by convex spherical lens

spherical lens

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Characteristics of image formed by concave spherical lens

spherical lens

 

Refraction of light

What do you know about the refraction of light? Can you think of an experiment that can practically demonstrate the refraction of light?

Let us device a fun experiment to explain the refraction of light. Take a bucket and draw a circle on the bottom using a waterproof marker. Fill up the bucket with water. Now try to drop a coin in such a way that it will drop exactly on the circle we have drawn. Pretty difficult to drop the coin exactly in the circle. Isn?t it! Why is it so difficult to drop the coin exactly within the circle? The light rays from the circle change its path when it enters the air from water. We have previously learned that the speed of light is different in a different medium. The speed of light is dependent on the density of the medium. The difference in the speed of light in various medium leads to the refraction of light.

There are a few rules of refraction of light.

  1. The refracted ray, incident ray and the normal to the interface between two media at the point of incidence, all lie on the same plane.
  2. For a given pair of media, the sine of the angle of incidence and the angle of refraction of light has a constant ratio. This law is called Snell?s law. This law can be represented by the following formula:-

Sine i/ Sine r= constant= 1n2

This constant is also called as the relative refractive index.

The refractive index is of two types- absolute refractive index and relative refractive index. Absolute refractive index (n) is derived from the following formula:-

n= speed of light in vacuum/ speed of light in medium = c/v

Consider a ray of light moving from one medium to another. The relative refractive index is the refractive index of one medium with respect to another medium. Therefore, relative refractive index is given by the following formula:-

1n2 = n2/n1= v2/v1

Here v2 and v1 is the speed of light in medium 2 and medium one respectively.

Can we predict the direction of refraction of light? When the light goes from a rarer medium to a denser medium, the ray of light bends towards normal while it bends away from normal when entering a rarer medium from a denser medium.

In conclusion, refraction of light is caused by the different speed of light in different mediums. Refraction of light is responsible for some wonderful optical phenomenon like the deep blue colour of the sky and twinkling of the stars. We shall learn more about these natural phenomena in subsequent articles.

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The human eye

The human eye is one of the five sense organs. It perceives the meaning of light. It is because of the human eye that we can see the varied and beautiful world around us. There are two eyes, located within a bony socket called the orbit. The bones of the skull and face form the boundaries of the orbital cavity. Within the orbital cavity, lies the eye, the extra-ocular muscles, loose connective tissue, blood vessels, nerves and the optic nerve.

The outermost covering of the human eyes is sclera, a thick, fibrous sheath. It functions to protect the eyeball from injury. The white colour of the eye is because of the sclera.

The cornea is the transparent portion of the eye that light to enter the eye. ?In previous chapters, we have learned about refraction. The cornea can be considered to be a refractive medium that brings the light rays to focus. Most of the refraction occurs at the out surface of the cornea.

human eye

Human eye: A cross-section.

The Iris, a muscular diaphragm, controls the entry of light into the human eye. How does the Iris monitor the entry of light into the human eye? Iris does so by controlling the size of the pupil, a small aperture. Have you noted what happens when you shine a torch into the eye? The pupil constricts, thus reducing the amount of light entering the human eye.

Immediately behind the Iris, lies the lens. The lens is flattened towards the front and it is suspended in the eye by muscles called the ciliary muscles. These muscles help with the process of adaptation. The ciliary muscles can increase or decrease the focal length of the lens to enable the eye to focus on objects across a broad range of focal lengths.

The light from a source is refracted by the cornea and the lens and is brought to focus on the light sensitive layer of the human eye- the retina.The retina contains two types light sensitive cells- the rods and cones. The rods, numbering 120 million are more numerous and are more sensitive to light. On the other hand, cones, numbering 6-7 million sense colour. The cones are concentrated around the centre of the retina, an area called the optic disc. Within the optic disc lies the fovea. Cones are present in the highest concentration in the fovea. Therefore, colour perception is best at the fovea.

The light that is refracted by the cornea and the lens forms an inverted real image over the retina. The image is transmitted to the occipital lobe of the brain by the visual pathways comprising the two optic nerves, optic tracts and their projections. The human brain processes the signals. Therefore, we only see the erect images.

Thus, the human eye behaves like a camera for all purposes. There is one difference though- the human eye can appreciate the depth of field, which a camera sorely lacks.

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Mirrors: Types and properties

Every one of us has used a mirror. We use mirrors to look at ourselves while we get ready in the morning. Mirrors in vehicles help us see the road behind, and sophisticated equipment like telescopes and solar panels also use mirrors. So, what is a mirror?

Simply put, a mirror is any surface that can reflect light and create a clear image. Have you ever looked at your face in a spoon? We have all done this at the dining table. Here, the curved surface of the spoon acts as a mirror. So, how does your face look on the spoon? It depends on which side of the spoon is being looked at. Your face will look different on both the sides of the spoon because of the unique properties of each surface.

Mirrors are of two types- spherical and plane.

Spherical mirrors are of two kinds- convex and concave.

The reflecting surface of a spherical mirror can be considered to be a part of a sphere. The reflecting surface of a concave mirror is curved inside while it is curved outside in case of a convex mirror.

.There are a few terms associated with spherical mirrors. You will come to these terms when spherical mirrors are discussed.

images

  1. Centre- As discussed previously, the reflecting surface of a mirror is a part of a sphere. This sphere has a centre. The point in space that corresponds to the heart of the sphere is called as the centre of curvature of the mirror. The centre of curvature is represented by the letter ?C?. The centre of curvature is not part of the mirror. In a concave mirror, the centre of curvature lies in front of the mirror while it lies behind the reflecting surface in a convex mirror.
  2. Pole of the mirror- The central point on a mirror is called the pole of the mirror.
  3. Principal axis- A line drawn from the centre of curvature to the pole of the mirror is the principal axis of the mirror.
  4. The radius of curvature- The distance from the centre of curvature to the pole of the mirror is called as the radius of curvature. This value is the same as the radius of the sphere of which the mirror is a part of.
  5. Principal focus- This is the point where parallel rays of light are brought to a focus by the mirror. In a concave mirror, this point lies in front of the mirror. In a convex mirror, it lies behind the reflecting surface of the mirror.

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What is Light? The various theories of light.

Light is of considerable significance in our life. It helps us see the objects around us. Many beautiful phenomena like the rainbow and the twinkling of stars are a result of the properties of light. And the light is required for the function of one of the most important sense organs in humans- the eye. So, have you ever wondered what is light? We know the sun lights up the world with its rays. We know that we can switch on an electric bulb in the night and voila, we can once again see the world around us!

So, how does all this happen? All things, both living and non-living reflect light to varying degrees. When the light reflected from a surface falls on the retina, an image of that object is created by our eyes. This image is transmitted to the brain, and thus we see!

The earliest theories on the nature of light date back to 300 BC. Elucid described the properties of light in his book-The Optica. He demonstrated that light travels in a straight line, and he was one of the first to study reflection mathematically.

In the 1600?s Pierre Gassendi proposed the particle theory. Gassendi?s work was carried forward by Sir Issac Newton, who in 1704, published his observations on the nature of light. Sir Newton?s view could help predict the reflection. However, to predict refraction, Newton used a flawed argument that light entering a denser medium accelerated as the gravitational pull was more. Another major problem with the particle theory was that it could not explain the phenomena of diffraction. Newton explained diffraction by assuming that light creates a localised wave in the aether.

During the 1600?s, another theory postulated- the wave theory. One of the earliest proponents of this theory was Robert Hooke. He published his Pulse Theory in 1665. Here, he argued that light is a wave whose vibrations are perpendicular to the direction of propagation. He compared the waves of light to the waves in the water. The wave theory was carried forward by scientists like Leonhard Euler, Christiaan Huygens,?Augustin-Jean Fresnel, and Sim?on Denis Poisson. The wave theory could explain both diffraction and polarisation, but waves require a medium to propagate. Huygens postulated that a hypothetical substance-?luminiferous aether is the medium through which light travels. However, the presence of the luminiferous aether was disproved by the Michelson?Morley experiment.

There were other problems with both the theories. The particle theory predicted that light would travel faster in a denser medium while the wave theory suggested the opposite. This debate was finally laid to rest by Leon Foucault, whose observations on the speed of light supported the wave theory of light. However, the particle theory of light partly re-emerged with the postulation of the electromagnetic theory of light. We shall learn more about the electromagnetic theory of light in a later article.

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The Electromagnetic Theory of Light

The Electromagnetic Theory of Light was first propounded by Michael Faraday in 1845. He discovered that when linearly polarised light passes through a magnetic field, its plane of polarisation rotates. This phenomenon is now called the Faraday rotation. Faraday postulated that light is a high-frequency electromagnetic vibration that can travel without the help of a medium.

Faraday?s work was carried forward by James Clerk Maxwell. Maxwell discovered that electromagnetic waves can travel through space at a speed that is similar to the measured speed of light. His discovery led him to postulate that light was some electromagnetic radiation. In 1873, Maxwell published his work- the Maxwell Equations, where is described the behaviour of electric and magnetic fields mathematically.

Maxwell?s electromagnetic theory of light was confirmed experimentally by Hertz, who in the late 1800?s produced and detected radio waves in the laboratory. He demonstrated that the radio waves were similar to light in all properties- reflection, refractions, diffraction and interference.

The work of Maxwell and Hertz has played a significant role in the development of radio, TV, wireless communication and radars. However, the electromagnetic theory of light does not explain certain phenomena like the spectral lines.

In the early 19th century, Max Planck suggested that although the light is a wave, it could gain or lose energy about its frequency. He called these clumps of light as quanta (Latin for? how much?). ?Albert Einstein used this idea to explain his photoelectric effect. Finally, in 1926, Lewis renamed these quanta as photons.

Thus was born the theory of quantum mechanics. Quantum theory imagines light to be both a particle and a wave. It also imagines of light as phenomena that are neither a particle nor a wave. Light can be described by mathematical formulae appropriate for both particles and waves. Thus, the actual nature of light is still beyond the comprehension of man.

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