Light and Optics

This chapter asks which lenses correct long-sightedness and short-sightedness, and which factor besides thickness affects the focal length of a lens p. 200.

7.1 Formation of Images by Lenses

A lens is a transparent medium such as glass which has one or two curved surfaces, and lenses are divided into convex lenses and concave lenses p. 202. Light rays converge after passing through a convex lens and diverge after passing through a concave lens p. 202. Therefore, a convex lens is known as a converging lens while a concave lens is known as a diverging lens p. 202.

For a convex lens, the focal point, F, is where light rays parallel to the principal axis converge after passing through the lens p. 203. For a concave lens, the diverging rays are extrapolated backwards, and the point where they intersect is the focal point p. 203. Activity 7.1 uses an Optical Ray Kit to show these properties and is best carried out in the dark p. 203. Three parallel light rays from the ray box are directed at the lens, and their point of intersection is marked as the focal point p. 204.

The optical centre, O, is the point at the centre of the lens, and light rays which pass through it do not refract p. 205. The principal axis passes through the optical centre and the focal point, while the axis of lens passes through the optical centre perpendicular to the principal axis p. 205. Focal length, f, is the distance between the focal point and the optical centre, object distance, u, is the distance between the object and the optical centre, and image distance, v, is the distance between the image and the optical centre p. 205.

In Activity 7.2, a convex lens is pointed at a distant object through an open window because light rays from a distant object are parallel p. 206. The white screen is adjusted until a sharp image forms, and the distance between the centre of the lens and the screen is the focal length p. 206. The position and characteristics of images can also be found using ray diagrams with two principal light rays p. 206.

For a convex lens, a ray parallel to the principal axis refracts and passes through the focal point p. 207. For a concave lens, a ray parallel to the principal axis refracts and appears to come from the focal point p. 207. For both lenses, a ray heading towards the optical centre continues in a straight line without refracting p. 207.

For a convex lens, an object further than 2F gives a real, inverted, diminished image between F and 2F p. 208. An object at 2F gives a real, inverted image at 2F of the same size as the object p. 208. An object between F and 2F gives a real, inverted, magnified image further than 2F p. 208. An object at F gives an image at infinity, and an object between F and the optical centre gives a virtual, upright, magnified image, which is how a magnifying glass is used p. 208. For a concave lens, the image for any object distance is virtual, upright, diminished and positioned between the object and the concave lens p. 209.

7.2 Optical Instruments

The function of optical instruments is related to whether the image is real or virtual and to the size of the image formed by the lens p. 210. In a microscope, the objective lens forms a real, inverted, magnified image of an object between F and 2F p. 210. The eyepiece then acts on an object between F and the optical centre to form a virtual, upright, magnified image p. 210. The magnifying power of a microscope equals the magnifying power of the objective lens multiplied by the magnifying power of the eyepiece p. 211. An objective lens of 40 times and an eyepiece of 4 times give a magnifying power of 160 times p. 211.

In a telescope, the objective lens forms a real, inverted, diminished image at F of an object at infinity p. 212. The eyepiece, with this image at its F, forms a virtual, upright, magnified final image at infinity p. 212. In normal adjustment, the distance between the objective lens and eyepiece is fₒ + fₑ so that the image can be viewed more comfortably p. 212. In Activity 7.3, a simple telescope model is built in a hollow paper cylinder using a convex lens with fₒ ≥ 10 cm and a convex lens with fₑ ≤ 2 cm p. 213.

Lenses in smartphones and closed-circuit television (CCTV) are only several millimetres thick, and flat lenses can be only several microns thick, where 1 micron = 0.001 mm p. 214. In a DSLR camera, the shorter the focal length of the lens, the wider the field of vision p. 214. Activity 7.4 studies lenses in cameras, smartphones, LCD projectors, spectacles, magnifying glasses and CCTV p. 215. A water lens can function as a magnifying glass p. 215.