Lenses

Lenses are those circular objects which looks like a cat's eye slit when viewed from the sides. We know that there are two kinds of spherical mirrors, concave mirror (which converges light at the focus) and convex mirror (which diverges light). Similarly, in case of lenses there are two major types concave and convex (other types are plano-concave, biconcave and convexo-concave and vice-versa). In case of lenses, convex lens converges light rays whereas concave lenses diverges light rays. In mirrors we polish and silver a surface so as to reflect light coming from an object but lenses require polishing of two spherical surfaces accurately so as to refract light from the object. We know that reflection means bouncing back of light from a shiny (mostly), polished surface. What is this refraction? Refraction means bending of light rays. But light travels in a straight line. What causes it to bend? The answer is change of density of medium. But it doesn't bend just anyhow. It bends from a normal through a certain angle.


As we can see normal means a perpendicular drawn to the interface of two media. When light travels from a rarer medium to a denser medium it bends towards the normal and vice versa for light travelling from a denser medium to the rarer. The ability of a medium to bend light rays is its refractive index which has no units and is calculated by dividing sin of the angle of incidence ( sin[i] ) to the sin of the angle of refraction ( sin[r] ). In a lens the surface is curved and hence normal drawn to the surface are not parallel to each other but are intersecting. Thus, refraction of light by a lens occurs like this and according to the shape of the spherical surface it either converges or diverges light rays.

 The image seen from refraction varies according to the distance of the object from the mirror. The lens formula is :

1/v-1/u=1/f

Where, v = Distance of image from optical centre of lens

             u = Distance of object from optical centre of lens

and       f = Focal length of lens


Refraction of light is the reason we see a bent (broken?) spoon when it is kept in a glass of water. The image produced depends on the distance of the object. the cases are:

Case 1: the object is located beyond the 2F (distance equal to twice the focal length) point 

Case 2: the object is located at the 2F point 

Case 3: the object is located between the 2F point and the focal point (F)

Case 4: the object is located at the focal point (F) 

Case 5: the object is located in front of the focal point (F)
And the results are:

Result 1: the image will always be located somewhere in between the 2F point and the focal point (F) on the other side of the lens. The image will be real and inverted.

Result 2: the image will also be located at the 2F point on the other side of the lens. The image will be real and inverted.

Result 3: the image will be located beyond the 2F point on the other side of the lens.The image will be real and inverted.

Result 4: For the case of the object located at the focal point (F), the light rays neither converge nor diverge after refracting through the lens.

Result 5: the image will always be located somewhere on the same side of the lens as the object. The image will be virtual and erect.
The lenses are also used for focusing on minute near objects by use of microscopes and at far away stars, galaxies, etc by use of the telescope.

The spectacles we wear work on this principle. Far-sightedness, also known as long-sightedness and hyperopia, is a condition of the eye in which light is focused behind, instead of on, the retina. This causes close objects to be blurry, while far objects may appear normal. The lenses used for this condition are convex lenses which increases the power of convergence of the crystalline eye lens. The condition also occurs if the eyeball is too small. Near-sightedness, also known as short-sightedness and myopia, is a condition of the eye where light focuses in front of, instead of on, the retina. This causes distant objects to be blurry while close objects appear normal. this condition also occurs if the eyeball is lengthened. For this condition, concave lenses are used so that light reaching the eye lens diverges a little and then the eye lens converges it so that it falls on the retina. Presbyopia is a condition associated with aging of the eye that results in progressively worsening ability to focus clearly on close objects. This is because of hardening of the eye lens which does not remain flexible enough to get thinner and focus it on the retina. Lenses used in spectacles vary according to how much the light it converges or diverges. The formula for magnification is: 

D(1) / D(0) = f / [f - D(0)] = m

Where, D(1)= Distance of image from optical centre of lens

             D(0)= Distance of object from optical centre of lens

        

             m= Magnification power

and       f = Focal length of lens

By a simple trick with his/her glasses you can quickly tell whether a person is near-sighted or farsighted. A nearsighted person must wear diverging lenses, so print looks smaller if those lenses are held a few inches above the printed page. A farsighted person must wear converging lenses, and those will make the print appear larger.

While using lenses for the telescopes, the lens should be big so as to collect more light and its focal length should be small. But if the lens becomes thick the colours in white light will seperate (since different colours refract to different amounts. This cannot be observed in a glass slab since all the normals are parallel and the seperation of colours due to refraction is reversed when light leaves the glass slab) and form a colourful halo of light around celestial objects. This is called chromatic aberration. Also, the bigger the lens gets the harder it is to make it and use it in the telescope. For this, Sir Isaac Newton introduced a new type pf telescope, reflecting telescope. The refracting telescope used earlier would have two lenses whereas the one proposed by Sir Isaac Newton had a mirror. Moreover, the effort used to make a giant mirror for collecting light of celestial objects is lesser than to make a lens for the same purpose. The chromatic aberration was thus avoided. The diagram is as follows: