 |
| Summary |
|
 Ray optics is also called geometrical optics as it uses the geometry of straight-line paths (rays) to explain the optical phenomena. |
| |
| Ray optics, infact, is the limiting case of wave optics. This means for most practical purposes, we can ignore the deviation from straight-line path as postulated by wave theory. |
| |
|
The three types of sources of light are: thermal sources, gas discharge sources and luminescent sources. The standard luminosity curve of human eye shows that our eye is much more sensitive to green yellow region of the visible spectrum. |
| |
|
Photometry is a branch of Physics, which deals with the measurement of light energy. In this connection, four terms should be clearly understood. The terms are: |
| |
|
Luminous Flux (f) of a source is defined as the amount of visible light energy emitted per second by the source. It is measured in lumen. |
| |
|
Luminous Intensity or Illuminating Power (I) of a source is the amount of visible light energy emitted per second per unit solid angle by the source. It is measured in candela or candle power (C.P.) |
| |
|
Illuminance or Intensity of illumination (E) of a surface is the luminous flux incident normally on unit area of the surface. |
| |
 |
| |
 |
| |
 |
| |
| E is measured in lux or meter candle and photo or cm candle, 1 photo = 104 lux. |
| |
|
Luminance of a surface refers to brightness of the surface. It is the luminous flux reflected from unit area of the surface. It depends on illuminance (E) and the nature of the surface. |
| |
|
Efficiency of an electric light source is the ratio of output power of the source in the visible range to the input electric power fed to the source. It is measured in lumen /watt. |
| |
Laws
of photometry state that E a I;
 |
| |
| E a cosq, where q is the angle, which the incident light makes with normal to the surface at that point. |
| |
| Or |
| |
 |
| |
|
A photometer is an instrument, which is used for comparing the illuminating powers of two sources of light. When two surfaces of same nature are illuminated by two sources, they appear to be equally bright, as detected by human eye, then |
| |
 |
| |
 |
| |
r1 and r2 are measured to obtain 
. This is the basis we use in a Bunsen grease spot-photometer. |
| |
|
Reflection of light is the phenomenon of change in the path of light without any change in medium. |
| |
| A spherical mirror is a part of a hollow sphere whose one side is reflecting and other side is opaque. Two types of spherical mirrors are concave mirror and convex mirror. The centre of curvature (C) of spherical mirror is the centre of the sphere of which the mirror forms a part. Principal focus (F) of a spherical mirror is a point on the principal axis of the mirror at which rays incident on the mirror in a direction parallel to the principal axis actually meet or appear to diverge after reflection from the mirror. |
| |
|
While dealing with reflection at spherical mirrors, we use the following new Cartesian sign conventions: |
| |
| - All distances are measured from pole of spherical mirror. |
| |
| - The distances measured in the direction of incidence of light are taken as positive and vice-versa. |
| |
| - The heights measured upwards and perpendicular to the principal axis of the mirror are taken as positive and vice-versa. |
| |
|
In case of both the spherical mirrors, convex and concave, f = R/2. |
| |
| Also the mirror formula for both the mirrors is |
| |
 |
| |
| Where u is the distance of the object and v is the distance of the image from the pole of the mirror. |
| |
| Linear magnification in case of a spherical mirror is defined as the ratio of size image (h2) to the size of the object (h1). |
| |
| In a convex mirror, linear magnification is positive, because image is always virtual. |
| |
 |
| |
| In a concave mirror, magnification can be both positive or negative, depending on the type of image formed (virtual or real). |
| |
 |
| |
| Other formulae for magnification are |
| |
 |
| |
| Spherical mirrors have several applications. A convex mirror is used as reflector in street lamps. It is also used as a rear view mirror. A concave mirror is used as a reflector in search light, telescopes, solar cookers, and ophthalmoscope. They can also be used as trick mirrors. |
| |
|
Refraction of light is the phenomenon of change in the path of light, when it travels from one medium to another. |
| |
| When it travels from a rarer to a denser medium, a ray of light bends towards normal and while traveling from a denser to a rarer medium, a ray of light bends away from normal. This is because light travels slower in a denser medium than in a rarer medium. |
| |
| On account of refraction of light, a tank of water appears to be shallow as it is less deep than what it actually is. |
| |
| It is found that |
| |
 |
| |
| If i is angle of incidence, r is angle of refraction and m is refractive index of denser medium with respect to rarer medium, then according to Snell's law, |
| |
 |
| |
| (when light goes from rarer to denser medium). and |
| |
 |
| |
| (when light goes from denser to rarer medium). |
| |
| Further, refractive index of medium a with respect to medium b is represented by |
| |
 |
| |
 |
| |
|
Total internal reflection is a phenomenon of reflection of light on traveling from a denser medium to a rarer medium. |
| |
| Two essential conditions for the phenomenon of total internal reflection are: |
| |
| - Light should travel from a denser to a rarer medium. |
| |
| - Angle of incidence of denser medium should be greater than the critical angle for the pair of media in contact. |
| |
| The critical angle for a pair of media in contact is defined as the angle of incidence in the denser medium corresponding to which angle of refraction in the rarer medium is 900. It is represented by C. |
| |
| If m is refractive index of denser medium with respect to rarer medium, then |
| |
 |
| |
| Obviously, C would depend on colour of light. |
| |
| Some of the important applications of total internal reflection are brilliance of diamond, totally reflecting glass prisms, optical fibres, mirage (false appearance of water in deserts in hot summer season) etc., |
| |
|
A surface, which forms a part of a sphere of transparent refracting material, is called a spherical refracting surface. It may be convex or concave. In dealing with refraction at such surfaces, we use the same new Cartesian sign conventions as in the case of spherical mirrors. |
| |
| The formula governing refraction at a spherical surface when light travels from a rarer to a denser medium. |
| |
 |
| |
| (where u and v are distances of object and image respectively from the pole of the spherical surface and R is the radius of curvature of the surface). |
| |
| When light travels from a denser to a rarer medium, we have to interchange m1 and m2 in the above formula. |
| |
| The relation becomes: |
| |
 |
| |
 |
| |
 |
| |
|
A lens is bound by two spherical surfaces. Therefore, a ray of light suffers two refractions on passing through the lens. |
| |
| The lens maker's formula for both convex and concave lenses is |
| |
 |
| |
| (where R1 and R2 are radii of curvature of the two surfaces of the lens and m is refractive index of material of lens with respect to medium in which lens is placed). |
| |
| The relation governing u, v and g in case of both the lenses is |
| |
 |
| |
| Linear magnification (m) produced by a lens is the ratio of the size of image (h2) to the size of the object (h1). |
| |
| For concave lens, m is positive (when image is virtual) and m is negative (when image is real). |
| |
 |
| |
| For convex lens, m is positive (when image is virtual) and m is negative (when image is real). |
| |
 |
| |
| Power of a lens is defined as the ability of the lens to converge or diverge a beam of light falling on the lens. |
| |
| Power of lens is given by reciprocal of focal length of the lens i.e., |
| |
 |
| |
| When f = 1m, p = 1 dioptre |
| |
| For a converging lens or convex lens, P is + and for a diverging lens or concave lens, P is negative. |
| |
|
When two lenses of focal length f1, f2 and linear magnification m1 and m2 are placed in contact with each other, then for the combination, focal length F, power P and magnification m are given by |
| |
 |
| |
| P = P1 + P2 |
| |
| (Sum has to be taken with proper sign.) |
| |
| and m= m1 x m2 |
| |
|
On passing through a prism, a ray of light suffers two refractions. The net deviation (d) suffered by a ray in passing through a prism of small angle A is , |
| |
| d = (m - 1) A |
| |
| The deviation through the prism is minimum (dm) , when i1 = i2 and |
| |
| r1 = r2 |
| |
| From i1 + i2 = A + dm, i + i = A + dm |
| |
 |
| |
 |
| |
| If m is refractive index of material of prism, then from Snell's law, |
| |
 |
| |
| This formula is called prism formula. |
| |
|
Dispersion of light is the phenomenon of splitting of white light into its constituent colors on passing through a prism. The band of seven colors so obtained is called visible spectrum. |
| |
| The cause of dispersion is : as lv < lr ; therefore, mv > mr fm = d = (m - 1); dv > dr |
| |
| That is why violet colour is at the lower end of the spectrum. |
| |
|
Angular dispersion produced by a prism |
| |
 |
| |
| Dispersive power of prism |
| |
 |
| |
 |
| |
| Deviation (d) for yellow colour is mean of red and violet. i.e., |
| |
 |
| |
| Similarly, mean refractive index of material of prism for yellow colour is |
| |
 |
| |
|
A spectrometer is used for obtaining pure spectrum of a source in laboratory and calculation of m of material of prism and m of a transparent liquid. |
| |
| It consists of three parts: collimator, which provides a parallel beam of light; prism table for holding the prism and telescope for observing the spectrum and making measurements on it. |
| |
| The telescope is first set for parallel rays and then collimator is set for parallel rays. When prism is set in minimum deviation position, the spectrum seen is pure spectrum. Angle of prism (A) and angle of minimum deviation (dm) are measured and m of material of prism is calculated using prism formula. For m of a transparent liquid, we take a hollow prism with thin glass sides. Fill it with the liquid and measure and A of liquid prism, m of liquid is calculated using prism formula. |
| |
