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The laws of Physics Topics are used to explain everything from the smallest subatomic particles to the largest galaxies.
Refraction through spherical surface convex and concave
We have seen a palmist using a lens (called magnifying glass) for seeing the details of the lines of a person’s palm. A watch maker also uses a lens to see the extremely small parts of a watch clearly. In fact, lenses play a very important role in our everyday life. Lenses are used in making spectacles, cameras, microscopes, telescopes, film projectors, and many, many other optical instruments. We have already studied that the working of a mirror is based on the reflection of light rays from its surface.
The working of a lens is based on the refraction of light rays when they pass through it. We will now study the formation of images by lenses in detail. Before we do that, we should know the various types of spherical lenses and the terms like optical centre, principal axis, principal focus (or just focus), and focal length, etc., which are used in the study of refraction of light by lenses. These are discussed below.
A lens is a piece of transparent glass bound by two spherical surfaces. Figure. This is a micro- There are two types of lenses : Convex lens and Concave lens.
(i) A convex lens is thick at the centre but thinner at the edges. Figure making microscopes, shows a convex lens in which the two surfaces A and B are convex or bulging out at the centre.
(ii) A concave lens is thin in the middle but thicker at the edges. Figure shows a concave lens in which the two surfaces C and D are concave or bent inward.
Figure shows the side view of a convex lens. When we look at a convex lens from the front side, it looks like a piece of transparent spherical glass (round glass) having a bulge in the middle [see Figure]. We can feel the bulge in the middle of the convex lens by touching it. Similarly,
Figure shows the side view of a concave lens. When we look at a concave lens from the front side, it looks like a piece of transparent spherical glass (round glass) having a ‘depression’ in the middle [see Figure]. We can feel the depression in the middle of a concave lens by touching it.
Please note that the lenses (convex lens and concave lens) work on the refraction of light through them.
Optical Centre and Principal Axis of a Lens
The centre point of a lens is known as its optical centre. The optical centre of a lens is usually denoted by the letter C. In Figure, C is the optical centre of the convex lens. The optical centre of a lens has a property that a ray of light passing through it does not suffer any deviation and goes straight. The optical centre of a lens is sometimes also denoted by the letter O.
The principal axis of a lens is a line passing through the optical centre of the lens and perpendicular to both the faces of the lens. In Figure, the line F’F is the principal axis of the convex lens and it passes through the optical centre C.
Principal Focus and Focal Length of a Convex
Suppose a parallel beam of light rays falls on a convex lens as shown in Figure. These light rays are parallel to one another and also parallel to the axis of the lens. The incident rays pass through the convex lens and get refracted (or bent) according to the laws of refraction. All the rays, after passing through the convex lens, converge at the same point F on the other side (right side) of the lens. The point F is called principal focus (or just focus) of the convex lens. We can now say that: The principal focus of a convex lens is a point on its principal axis to which light rays parallel to the principal axis converge after passing through the lens.
In Figure, point F is the principal focus for the light rays coming from the left side. If the incident light rays fall on the convex lens from the right hand side, they will converge to a point F’ on the left side of the lens. Thus, F’ is the second focus of the convex lens. From this discussion we conclude that a lens has two foci. The two foci of a lens are at equal distances from the optical centre, one on either side of the lens (The word ‘foci’ is the plural form of ‘focus’). The two foci of a lens are usually denoted by the letters F and F’. Since all the light rays actually pass through the focus of a convex lens, therefore, a convex lens has real focus.
We are now in a position to define the focal length of a lens. The focal length of a lens is the distance between optical centre and principal focus of the lens. In Figure, the distance CF is the focal length of the convex lens. It should be noted that the distance CF’ is also equal to the focal length of the lens. The focal length of a lens is denoted by the letter f. The focal length of a lens depends on the refractive index of the glass from which it is made, and the curvature of its two surfaces. Higher the refractive index, shorter will be the focal length. Similarly, more the curvature, shorter is the focal length.
A convex lens is also known as a converging lens because it converges (brings to a point), a parallel beam of light rays passing through it (see Figure). The fact that a convex lens converges (or focusses) parallel rays of light to a single point can be shown as follows : Place a piece of paper on the ground in bright sunshine (see Figure). Hold a convex lens some distance above the piece of paper in such a way that a sharp image of the sun is formed on the piece of paper. Here the convex lens is converging the parallel rays of sunlight due to which the sun’s rays get concentrated on a small part of the paper (where image is formed). The heat energy of focussed sunlight rays burns a hole in the piece of paper (where sun’s image is formed). Please note that we should never look at the sun through a convex lens. It can damage our eyes permanently by focussing a lot of sunlight energy into our eyes.
Principal Focus and Focal Length of a Concave Lens
We have just studied that a convex lens converges a parallel beam of light rays. A concave lens has just the opposite effect on such rays of light. A concave lens diverges a parallel beam of light rays. The action of a concave lens on a parallel beam of light rays is shown in Figure. When a parallel beam of light rays falls on a concave lens, the rays will spread out (or diverge) after passing through the lens. Since the refracted rays are diverging away from one another, they do not actually meet at a point. The diverging rays when produced backwards (as shown by dotted lines in Figure) appear to meet at a point F on the left side of the lens.
To a person on the right hand side, the refracted rays appear to be diverging (or coming) from a point F on the principal axis of the concave lens. This point is the principal focus of the concave lens. Thus, the principal focus of a concave lens is a point on its principal axis from which light rays, originally parallel to the axis, appear to diverge after passing through the concave lens. In Figure, the parallel rays of light appear to be diverging from point F after refraction. So, F is the principal focus of the concave lens for the light rays coming from the left side.
Like a convex lens, a concave lens also has two foci, one on each side of the concave lens. For example, if the parallel rays fall on the concave lens from the right side, then they will appear to diverge from a point F’. Thus, F’ is the second focus of the concave lens. A concave lens is also known as a diverging lens because it diverges a parallel beam of light rays (see Figure). Since the light rays do not actually pass through the focus of a concave lens, a concave lens has a virtual focus. In Figure, the distance CF is the focal length of concave lens. The distance CF’ is also equal to the focal length.
A yet another term which is used in the study of spherical lenses is ‘aperture’. The aperture of a spherical lens (convex lens or concave lens) is the surface from which refraction of light takes place through the lens. The aperture of spherical lens is represented by its diameter. In most simple words, aperture tells us the size of the lens.
Rules for Obtaining Images Formed by Convex Lenses
When an object is placed in front of a convex lens, an image is formed. The image is formed at that point where at least two refracted light rays meet (or appear to meet). To find out the position and nature of the image formed by a convex lens, we will use only those two rays of light (coming from the top of the object) whose paths after refraction from the lens are known to us and easy to draw (the bottom of the object is always assumed to be on the principal axis of the lens). Any two of the following rays of light are usually used to locate the images formed by convex lenses. We call them rules for obtaining images in convex lenses.
Rule 1. A ray of light which is parallel to the principal axis of a convex lens, passes through its focus after refraction through the lens. This is shown in Figure. Here we have a convex lens L and its principal axis is X”Y’. Now, a ray of light AD (coming from an object) is parallel to the principal axis of the convex lens. It enters the convex lens and gets refracted (or bends) at point D inside it. After refraction its path changes, it passes through focus F and goes in the direction DX (see Figure).
Rule 2. A ray of light passing through the optical centre of a convex lens goes straight after refraction through the lens. It does not get deviated (or bent). This is shown in Figure. A ray of light AC is passing through the optical centre C of a convex lens. It goes straight in the direction CY after passing through the lens. It does not get deviated (or bent) from its original path (see Figure). Please note that a ray of light going along the principal axis of a convex lens also passes straight through the lens without any deviation.
In Figure, the principal axis of the convex lens is X’Y’. So, a ray of light going along the principal axis X’Y’ of this convex lens will also go straight (without bending). We should keep this point in mind because in drawing ray- diagrams, an object is always placed above the principal axis of a lens so that a ray of light coming from its bottom always goes straight through the lens (along the principal axis).
Rule 3. A ray of light passing through the focus of a convex lens becomes parallel to its principal axis after refraction through the lens. This rule is just the reverse case of the first rule and it is shown in Figure. Flere a ray of light AD (coming from the object) is passing through the focus F’ of the convex lens. It enters the convex lens and gets refracted (or bends) at point D inside it. After passing through the convex lens, it becomes parallel to the principal axis of the lens and goes in the direction DX (see Figure). Please note that in this case the ray of light has to pass through the second focus F’ of the convex lens which lies on its left side.
We should remember the paths of the three rays of light described above because these will be used to construct ray-diagrams for finding the position and nature of images formed by convex lenses. At any given time, we will use only two of the above three types of light rays to find the position of image formed by a convex lens. We will now discuss the various positions at which an object can be placed in front of a convex lens to form images.