Introductory physics: the lens

A spectacular application of the phenomenon of refraction (see previous post) is the lens. Just as a focusing mirror is used to obtain an image of a distant object (see post on mirrors), a lens is used to focus light by refraction. The difference is that the light is transmitted through a lens – it is refracted once entering the lens and again as it passes out again. Lenses are cut from parabolic surfaces in such a way that distant rays are brought to a focus at the focal point.

As with mirrors, there are two types of lenses, depending on the curvature of cut: a convex lens causes parallel rays of light to converge to a real focus, while a concave lens cause the light to appear to diverge from a virtual focus.

As with mirrors, the position of an image will depend on the distance of the object from the lens (but the image of a distant object will of course be at the focal point of the lens). Amazingly, the same equation applies: for an object a distance u from a lens of focal length f, the location v of the image can be found from the relation

1/u +  1/v =   1/f

(Note that for a distant object u = ∞ and hence v = f ). The magnification m of the image can be calcuated from the equation m =  –v/u, as before.

Applications

Lenses are used extensively in everyday life. The most common example is of course spectacles. No one knows when spectacles were first invented (12th century?), but they have been used throughout the ages to improve defective human eyesight.

Typically, spectacle lenses are concave (diverging) lenses are made from glass or plastic. This is because the most common eyesight defect is myopia (shortsightedness), a condition where the natural lens of the eye focuses too strongly i.e. an image is formed short of the retina. A diverging lens of the right strength placed in front of the eye will cause the image to be projected back on the retina as normal.

Concave (diverging) lens used to correct myopia

In the case of hyperopia (the longsightedness that occurs commonly in older people), the eye muscles are weakened and an image is formed beyond the retina; this is corrected by placing a convex (converging) lens in front of the eye in order to strengthen it i.e. shorten the focal length of the eye’s natural lens.

Converging lens used to correct longsightedness

A modern application is the contact lens: this operates on the same principle as above, but the lens is made of a soft fabric that can be worn directly on the pupil. A third option nowadays is laser surgery; in this case the focal length of the eye’s natural lens is adjusted directly (and permanently) by laser treatment.

Lenses and science

Lenses played a pivotal role in the development of science. In the 17th century, advances in lens technology led directly to the invention of the microscope, a device that revolutionized our view of the world of the very small: and to the development of the telescope, an invention that revolutionized our view of the solar system and ultimately the entire universe.

Exercises

1. If an object 5 cm high is placed 30 cm in front of a convex (converging) lens of focal length 20 cm, calculate the position and height of the image.  Is the image real or virtual?

2. As a shortsighted person ages, can the onset of longsightedness cancel myopia?