Ray Optics

We are able to read text on the screen/page. It is due to diffused refraction of light diffused reflection of light phenomenon of diffraction of light diffused dispersion of light The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Where should be the position of the object? (a) between the principal focus and the center of curvature (b) at the center of the curvature (c) beyond the center of curvature (d) between the pole of mirror and its principal focus. No matter how far you stand from a mirror, our image appears erect. The mirror is likely to be – (a) plane only (b) concave only (c) convex only (d) either plane or convex. We wish to obtain an upright image of an object using a concave mirror of focal length 15 cm. What should be the range of distance of the object from the mirror? What is the nature of the image? Is the image larger or smaller than the object? shows a light ray travelling from glass towards      water.  A light ray from air travels into a medium X as shown in       Fig.12.8. What is the refractive index of medium X. Fig.12.9 shows light  travelling from water into air.              What is the refractive index of water?  An object is at the bottom of a lake, as shown in Fig. 12.12.       The water is crystal clear.clear.           Draw a ray diagram to show where the object will be seen       by the observer.  What is the path of the light ray after that?  Colour printing works because white paper reflects all colours in equal amounts. Inks filter out the other colours; for example, blue ink absorbs red and green light and transmits the blue light reflected from the paper. To achieve a good range of colours, three colours of ink are used: cyan (blue) magenta (pink) and yellow. In theory, this can produce all colours, but in practice black ink is used to get better blacks, and to make black and white printing easier. This is called subtractive colour (sometimes known as CMYK colour after the four colurs - K stands for black). Converting RGB values to CMYK was once quite a difficult software task. How does a rainbow formed?    Fig. 12.20 shows light rays from various angles incident       towards the s the lens centre.       What happens to the light rays after this?  Where should an object be placed in front of convex lens to get a real image of the size of the object? (a) at the principal focus of the lens (b) at twice the focal length (c) at infinity (d) between the optical center of the lens and its principal focus. One half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object?  Find the focal length of a lens of power –2.0 D. What type of lens is this? Chromatic aberration can be corrected using a chromatic doublet. This is a combination of two lenses, one convex and the other concave. The lenses are of different types of glass (crown glass & flint glass) . The pair are cemented together (not shown) using Canada Balsam glue. This has a refractive index mid-way between the two glass types. In any event, the glue layer is extremely thin and has little effect. Compound Microscope Telescope Newtonian Reflector The primary image from the parabolic mirror is directed at 45ofrom the principal axis by a plane (flat) mirror into an eyepiece located at the side of the telescope.   Cassegrain reflector In the Cassegrain reflector light from the primary mirror is reflected backwards from a secondary, convex mirror and directed through the middle of the mirror. here the image is further magnified by an eyepiece. The Cassegrain has an advantage over a Newtonian by having a large f-number (ratio of focal length to primary mirror diameter). This allows much greater magnification to be attained. One other important advantage is the length of the telescope. Cassegrains are much shorter, typically less than half the length.   Schmidt-Cassegrain telescope (SCT) Along with the other advantages of a Cassegrain, a SCT reduces spherical aberration to a minimum. it does this using a 'corrector plate'. This is a specially designed lens, having properties of both convex and concave lenses.    A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? 54 cm before the mirror 36 cm before the mirror 18 cm before the mirror It can be placed at any distance, before the mirror Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved? A small bulb is placed at the bottom of a tank containing water to a depth of d cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of water is . (Consider the bulb to be a point source.) A compound microscope consists of an objective lens of focal length 2.0 cm and an eyepiece of focal length 6.25 cm separated by a distance of 15 cm. How far from the objective should an object be placed in order to obtain the final image at (a) the least distance of distinct vision (25 cm), and (b) at infinity? What is the magnifying power of the microscope in each case? A virtual image, we always say, cannot be caught on a screen. Yet when we ‘see’ a virtual image, we are obviously bringing it on to the ‘screen’ (i.e., the retina) of our eye. Is there a contradiction?   The refractive index of diamond is much greater than that of ordinary glass. What is the range of angles of incidences within diamond for TIR to take place. (a) The angle subtended at the eye by an object is equal to the angle subtended at the eye by the virtual image produced by a magnifying glass. In what sense then does a magnifying glass provide angular magnification? (b) In viewing through a magnifying glass, one usually positions one’s eyes very close to the lens. Does angular magnification change if the eye is moved back? (c) Magnifying power of a simple microscope is inversely proportional to the focal length of the lens. What then stops us from using a convex lens of smaller and smaller focal length and achieving greater and greater magnifying power? (d) Why must both the objective and the eyepiece of a compound microscope have short focal lengths? (e) When viewing through a compound microscope, our eyes should be positioned not on the eyepiece but a short distance away from it for best viewing. Why? How much should be that short distance between the eye and eyepiece? Magnification is the ratio between the apparent size of the object as seen in its virtual image M=, and its actual size. It is given by the product of magnifications by the objective and the eyepiece. For example, with a 40× objective and a 10× eyepiece, the image is magnified 40× 10 or 400 times. Magnification may be enhanced by increasing the power of either or both the lens systems. Resolution is the capacity of the objective to distinguish between two close-set points in the specimen as separate entities in its image. The limit of resolution (γ) is the shortest distance between two adjacent points in the specimen or object for making them look separate from each other. The smaller the value of γ, the higher is the resolving power. Resolution depends solely upon the numerical aperture (NA) of the objective. NA measures the light collecting ability of the lens. The higher the NA of the objective, the greater is its ability to gather light, the smaller is its γ and the higher is its resolving power. Fig. 1.12: Collection of light by a lens Where n is the refractive index of the medium between the object (specimen) and the from lens of the objective, λ is the wavelength of light and θ is the semi-angle of the light cone accepted by the objective. In other words, θ is the angle between the outermost ray entering the front lens on any side and the optical axis of the lens (Fig. 1.12). Since θ cannot exceed 90˚ and n is 1 for air serving as the medium between the object and a dry objective, NA cannot surpass 1 and y cannot be less than of λ averaging 537nm. NA = n sin θ = 1×sin90˚ =1 γ = =  nm = 0.33μm In practice, however, θ is always less than 90° so that NA is always less than the refractive index n of the medium between the object and the objective. While working in air, NA does not exceed 0.95 and γ cannot be shorter than 0.35 μm. γ = =  nm = 0.35μm Fig. 1.13: Path of light through the dark-ground condenser of an ultramicroscopic. An oil immersion lens is formed by filling the space between the front lens of the objective and the object with cedarwood oil (n = 1.5). This may increase the NA of the objective upto 1.5 and may consequently enhance the resolving power, with γ dropping to 0.2μm, with white light. NA = n sinθ = 1.5 sin 90° =1.5 γ =  =  = nm = 0.2μm In practice, however, NA does not exceed 1.40 for an oil immersion lens and γ cannot be shorter than 0.23μm, because θ is practically always less than 90°. Because the resolving power of a microscope is limited by the NA of the objective, the magnifying action of the eyepiece cannot make such details visible as have not been separated in the real image formed by the objective. The eyepiece contributes nothing towards resolution; it can only multiply the magnification. If its magnifying power is enhanced beyond the resolving power of the objective, the magnified image fails to show further details and its quality deteriorates (empty magnification). As a general rule, the total magnification by the eyepiece and the objective must not exceed 1000times the NA of the latter. Thus, with an oil immersion lens (NA = 1.40), the total magnification should not exceed 1400 to avoid empty magnification. b d d angle of incidence, i = 90° 32° = 58°      angle of refraction, r = 90° - 56° = 34°    refractive index, n = sin i                                            sin r                                           = sin 58° .                                           sin 34°5                                         = 0.848                                            0.559                                           = 1.52  Range of the distance of the object = 0 to 15 cm from the pole of the mirror.  Nature of the image = virtual, upright and larger than the object. b Yes, the lens will produce a complete image of the object although one half of a convex lens is covered with a black paper Mohammad Abdul Mumeed, Senior Secondary Teacher in Physics, I.I.S.R. 18