Ray Optics Mr Rishi Gopie
Ray Optics Nature of light Light is a form of energy which affects the human eye in such a way as to cause the sensation of sight. Visible light is a range of electromagnetic waves which occupy a very small part of the much larger electromagnetic spectrum. Diag. (1) Visible Light is emitted by luminous bodies- such as the sun, activated filament and fluorescent bulbs/tubes and candle flies. However light is reflected by non- luminous bodies such as the moon, a table, a chair, a wall etc. Light is usually represented by rays and each ray is represented by a straight line. An arrowhead placed on the line indicates the direction of the ray. A collection of rays, represented by several lines together, is called a beam. Consider three types of rays/beams Page 2 of 22
i) A parallel beam consisting of parallel rays ii) Diag. 2 A divergent beam, consisting of diverging rays Diag. 3 Page 3 of 22
iii) A convergent beam, consisting of converging rays Diag. 4 Page 4 of 22
The general properties of light include i) The rectilinear propagation of light, i.e. light travels in straight lines. This property is demonstrated by i. the formation of shadows including eclipses, and ii. The formation of images in pinhole cameras. ii) The reflection of light. This property is demonstrated by the action of mirrors in the formation of images of objects. iii) The refraction of light. This property is demonstrated by the action of rectangular and triangular prisms and by the action of lenses in the formation of images of objects. iv) The dispersion of (polychromatic) light. This property is demonstrated by rainbow formation. Page 5 of 22
Consider shadow formation RECTILINEAR PROPAGATION OF LIGHT i) Using an extended source of light Diag. 5 Page 6 of 22
ii) Using a point source of light Diag. 6 Page 7 of 22
The formation of the shadow of a planet is called an eclipse. Consider a) A solar eclipse (by the moon of the sun, i.e. the formation of the shadow of the moon on the earth as the moon comes between the earth and the sun and blocks all or part of the sun`s light from various locations of the earth`s surface that is facing the sun. Diag. 7 Page 8 of 22
Consider also Diag. 8 b) A lunar eclipse (by the earth, i.e. the formation of the shadow of the earth on the moon as the earth comes between the sun and the moon and blocks all or part of the Sun s light from various locations on the moon s surface that is facing the sun and the earth. Also there is no moonlight on the nightside of the earth although the moon in on that side. Diag. 9 Page 9 of 22
Reflection of Light When light is incident on a surface, some of the incident light maybe absorbed by the surface( and become internal energy), some maybe transmitted by the surface and some may be reflected by the surface. The nature of the surface determines which of these predominates- for instance, a dark, dull, rough, opaque surface will absorb most of the incident light, a transparent or translucent surface will transmit a significant proportion of the incident light; and a bright, smooth, shiny surface will reflect most of the incident light. Most surfaces reflect some of the light that is incident on them but because these surfaces are usually rough the reflection is irregular and diffuse. Some surfaces are very smooth and reflect incident light very efficiently such surfaces are called mirrors. Consider the laws of reflection 1) The incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane 2) The angle of incidence is equal to the angle of reflection. The behaviour of a mirror depends on its shape Consider examples: a) A plane mirror Diag. 10 Page 10 of 22
b) Curved Mirrors i) A convex mirror Parallel incident rays are spread out after reflection, i.e. they become divergent, also the application of the principle of reversibility of light indicates that the mirror gives a wide field of view- making it useful as a rear view mirror in a vehicle, say and as a security mirror, in a super market say. ii) Diag. 11 A concave mirror Parallel incident rays are converged to more than one focus after reflection Diag. 12 Page 11 of 22
iii) A parabolic mirror Parallel incident rays are converged to only one focus after reflection. So it is more efficient at concentrating the reflected rays, than is a concave mirror. Diag. 13 Consider a ray diagram showing the formation of an image in a plane mirror through reflection; Diag. 13b Page 12 of 22
The characteristics of such an image include: i) It is a virtual image, i.e. one which cannot be produced on a screen and its location (since the light rays do not actually pass through its location they only appear to do so. A real image, on the other hand, is one which can be produced on a screen since the rays actually do pass through its location. ii) The image distance (v) is equal to the object distance (u) iii) The image has the same size as the object (i.e. its magnification is 1) iv) The image is the same way up as the object, i.e. erect (with respect to the object). v) The image is laterally inverted with respect to the object. Such a virtual image can be located in practice by employing the method 0f no parallax ( say using optical pins are as the object in front the mirror and another as a search pin behind the mirror to locate the position of the virtual image. Page 13 of 22
REFRACTION OF LIGHT Principle laws Prisms Refraction can occur when light is incident on the boundary between two different optical media when light is incident on such a boundary a change in speed (and wavelength) of the light always occur. Refraction occurs once the light is incident on the boundary obliquely (i.e. at an angle of incidence that is not zero degrees or once the light is incident normally). Refraction means that the light undergoes a change in direction, i.e. it is bent or refracted, in addition to undergoing a change in speed (and wavelength) When light travels from a less dense medium (such as air) to a denser medium (such as water or glass) it is refracted towards the normal and its speed (and wavelength) decreases. However, when light travels from a denser medium to a less dense medium then it is bent or refracted away from the normal and its speed (and wavelength) increases. The laws of refraction states that 1) The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane. 2) The ratio of the sine of the angle of incidence (in the less dense medium) to the sine of the angle of refraction (in the denser medium) is a constant called the refractive index of the (denser) medium (when the less dense medium is air or a vacuum. This is known as Snell`s Law. Consider ray diagrams showing the passage of light through a medium in the form of a; Page 14 of 22
i) Rectangular Prism Diag. 14 Page 15 of 22
ii) Triangular Prism Diag. 15 Page 16 of 22
Refractive index of denser medium, n = sin i/sin r, From Snell`s law: Where, i is the angle of incidence in the less dense medium (such as air or a vacuum) r is the angle of refraction in the denser medium In a situation where, in fact I is in the denser medium and r is in the less dense medium then the principle of reversibility of light must be applied and the locations of I and r will be exchanged Then Snell`s law can be applied Note also, that: Refractive index of a denser medium, n = speed or wavelength of light in less dense medium (such as air or a vacuum)/ speed or wavelength of light in a denser medium While both speed and wavelength change when waves (such as light) travel from one medium to another the frequency of the wave remains constant. Examples of observations that illustrate the refraction of light include: i) That a straight object such as a stick or ruler appears to be bent when partly immersed in water ii) That the bottom of a pool of water (or an object on the bottom of the pool appears to be closer to an observer from above that it actually is. Page 17 of 22
Diag. 16 Page 18 of 22
The Critical Angle (c) is that angle of incidence, in the denser medium that produces an angle of refraction equal to 90⁰ in the less dense medium. Note: n =1/ sin c and sin c = 1/n The two conditions necessary for total internal reflection to occur are: i) The ray (or waves) must be travelling from a denser medium towards a less dense medium, and ii) The angle of incidence, in the denser medium, must be greater than the critical angle. Applications of total internal reflection include: i) Rotation of light through 90⁰ and/0r 180⁰ using triangular prisms for instance in binoculars and in periscopes ii) Transmission of light along light pipes in the process of fibre optics which is used in telecommunications for instance. Page 19 of 22
Refraction at curved surfaces Consider the action of a: Convex or converging lens When parallel rays are incident on such a lens they emerge as converging rays which are brought to a focus (F) in the focal plane of the lens on the other (i.e. emergent) side of the lens. Diag. 17 Concave or diverging lens When parallel rays are incident on such a lens they emerge as diverging rays which appear to diverge from a point (f) in the focal plane of the same (i.e. incident) side of the lens. Diag. 18 Page 20 of 22
Consider the various features associated with a lens: Diag. 19 O is the optical centre of the lens (i.e. the point that represents the centre of its diameter and the centre of its thickness). It is the point of intersection of the principal axis and the optical plane or line. The principal axis of a lens (of which the line FOF is part) is the straight line, through the optical centre, that is perpendicular to its optical plane/line and to its focal planes/lines. F is the focal point or principal focus of the lens one on either side of the lens and both equidistant from the lens. It is the point at the intersection of a focal plane/line and the principal axis. It is the point to which incident rays which are parallel to the principal axis (as to one another) would be converged after passing through a converging lens. It is also the point from which incident rays which are parallel to the principal axis (and to one another) would appear to diverge after passing through a diverging lens. f is the focal length of the lens one of either side of the lens and equal to one another, if is the linear distance between a focal plane/line and the optical plane/line of the lens, (e.g. The linear distance between the focal point or principal focus, F, and the optical centre, O) Parallel rays that are incident on a converging or convex lens are converged to a point in the focal plane or line of the lens, on the emergent side. Parallel rays that are incident on a diverging or concave lens emerge as diverging rays which appear to diverge from a point in the focal plane/line of the lens on the incident side Rays incident on the optical centre of a lens pass straight on (without being refracted.) Page 21 of 22
The thicker a lens or the greater the refractive index of the material of which it is made the shorter the focal length of the lens. A lens forms an image by the refraction of incident rays from an object (as opposed to a mirror which forms an image by reflection of the incident rays from the object). The linear distance an object and the optical plane line is referred to as the object distance (symbol u). The linear distance between an image and the optical plane/line is referred to as the image distance (symbol v) The linear magnification of an image is given by: Magnification = height of image/height of object And by Magnification = image distance, v/object distance,u Page 22 of 22