PHY121 Lecture Note 2 PDF

Lenses  LENSES A lens is a piece of any transparent material (like glass) with two faces, of which at least one is curved. The center of such a sphere is called center of curvature (C). The center of the lens is called optical center (O). The line passing through the...

Lenses  LENSES A lens is a piece of any transparent material (like glass) with two faces, of which at least one is curved. The center of such a sphere is called center of curvature (C). The center of the lens is called optical center (O). The line passing through the optical center and center of curvature of the faces of the lens is called principal axis or optical axis.  Types of lenses There are two types of lenses; convex lens or converging lens and concave lens or diverging lens. A convex lens is thicker in the middle and thinner at the edges. A concave lens is thinner in the middle and thicker at the edges.  Real or virtual Enlarged or Reduced Erect or Inverted  Ray Diagram for Convex Lens Principal Axis A parallel ray refracts through the focal point. A ray through the center of the lens continues straight. A ray coming through the focal point, refracts parallel to the principal axis.  Ray Diagram for Concave Lens Object Image The image formed by concave lens is: Virtual Reduced upright  THE LENSE FORMULAR While a ray diagrams provide useful information about object- image relationship, yet fail to provide the information in a qualitative form. Hence to obtain a numerical information. The Lens equation expresses the quantitative relationship between the object distance (𝑑𝑜 ) the image distance (𝑑𝑖 ) and the focal length (f). The equation is stated as follows: 1 1 1 = + 𝑓 𝑑𝑜 𝑑𝑖  The Magnification Equation relates the ratio of the image distance and object distance to the ratio of the image height ( ℎ𝑖 ) and object height( ℎ𝑜 ). The magnification equation is stated as follows: ℎ𝑖 𝑑𝑖 𝑚= =− ℎ𝑜 𝑑𝑜 The Power of a lens is defined to be the inverse of focal length: 1 𝑃= 𝑓 The power of a lens is positive if it is converging and negative if it is diverging. Lens Power is measured in diopters, D: 1𝐷 = 1𝑚−1 EXAMPLE: An object of height 3 cm, is placed 12 cm in front of a diverging lens with a focal length of – 7.9 cm. a) Use ray tracing to form the image b) Use the thin lens equations to find the image distance and size 1 1 1 1 1 1 = +  = +  di = −4.8cm f d o di −7.9 12 di di hi = −  hi = − ( −4.8 )( 3) = 1.2cm do ho (12 ) Practice Problems Problem 1: A 4.00 cm light bulb is placed a distance of 45.7 cm from a double convex lens having a focal length of 15.2 cm. Determine the image distance and the image size. Problem 2: A 4.00 cm light bulb is placed a distance of 8.30 cm from a double convex lens having a focal length of 15.2 cm. Determine the image distance and the image size. Problem 3: An object of height 4.0cm is placed a distance of 35.5 cm from a diverging lens having a focal length of -12.2 cm. Determine the image distance and the image size. OPTICAL INSTRUMENTS  The Microscope The objective has short focal distance. The object is placed just beyond the focal point. A real, inverted, enlarged, image is formed, at or near the focus of the eyepiece. The eyepiece works as a magnifier, producing a further magnified image. The distance between the lenses is larger than the sum of focal lengths. The total magnification is the product of each lens magnification. M  - (di / fobjective) (N / feyepiece)  The Human Eye The eye produces a real, inverted image in the retina. The Ciliary muscles change the shape of the lens, adjusting the focal length according to the object distance. The amount of light that enters the eye is controlled by the iris, that expands or contracts to adjust the pupil size  The Camera The camera forms a real, and inverted image, on a photographic film, or a solid state sensor The camera focuses by moving the lens back and forth. The aperture of the camera can be adjusted: focal length f f - number = = Small f-number aperture diameter D  large aperture The amount of light that enters the camera is controlled by the f-number (i.e 5.6) and the shutter speed (i.e.1/250).  The Magnifying Glass A magnifying glass is a convex lens that is used to produce a magnified image of an object. Object at near point:   ho / N If a lens with focal distance f (f < N), is placed in front of the eye, and the object is placed at f, the image forms at infinite, with angular size ’  ho / f. Since f < N  ’  , and the object appears magnified. Angular magnification: M = ’ /   N / f Tan     The Telescope A telescope is a device used to form a magnified images of distance object. Telescopes deal with objects that are infinitely far away. The image formed by the objective is at its focal point, (and at the focal point of the eyepiece). The eyepiece works as a magnifier, producing a further enlarged image. The distance between lenses is about the sum of the focal lengths. The angular magnification is M = ’ /  = fobjective / feyepiece DEFECTS OF VISION  DEFECTS OF VISION COMMON DEFECTS OF VISION There are mainly three common defects of vision. These are: Myopia or near-sightedness Hyperopia or far-sightedness Astigmatism  MYOPIA Myopia is also known as near-sightedness A person with myopia can see nearby objects clearly but cannot see distant objects distinctly. A person with this defect has the far point nearer than infinity. Such a person may see clearly up to a distance of a few meters. In a myopic eye, the image of a distant object is formed in front of the retina and not at the retina itself. CAUSES OF MYOPIA This defect may arise due to: (i) excessive curvature of the eye lens (ii) elongation of the eyeball.  CORRECTION OF MYOPIA This defect can be corrected by using a concave lens of suitable power. A concave lens of suitable power will bring the image back on to the retina and thus the defect is corrected.  HYPEROPIA Hyperopia is also known as far sightedness. A person with hyperopia can see distant objects clearly but cannot see nearby objects distinctly. CAUSES OF DEFECT This defect arises either because (i) the focal length of the eye lens is too long (ii) the eyeball has become too small.  Correction of Hyperopia This defect can be corrected by using a convex lens of appropriate power. Eye-glasses with converging lenses provide the additional focusing power required for forming the image on the retina.  Astigmatism Astigmatism is a defect that create asymmetric blur in the vision due to the irregular corneal curvature/shape or lens. Due to this condition the light rays that enter the eye fail to converge at a single focal point on the retina and form two foci instead. The lack of a single focus point results in the formation of blurred images on the retina.  CORRECTION OF ASTIGMATISM One of the most common ways to fix an astigmatism, glasses contain a cylindrical lens that compensates for the uneven curves in your cornea or lens.  BIFOCAL LENSES Sometimes, a person may suffer from both myopia and hypermetropia. Such people often require bifocal lenses. STRUCTURE OF BIFOCAL LENSES A common type of bi-focal lenses consists of both concave and convex lenses. The upper portion consists of a concave lens. It facilitates distant vision. The lower part is a convex lens. It facilitates near vision. Example A person having a myopic eye uses concave lens of focal length 50cm. What is the power of the lens? Solution: Focal length of a concave lens is always negative therefore −50 𝑓 = −50𝑐𝑚 → = −0.5𝑚 100 1 𝑝𝑜𝑤𝑒𝑟 𝑜𝑓 𝑎 𝑙𝑒𝑛𝑠 = 𝑓𝑜𝑐𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ 1 𝑝𝑜𝑤𝑒𝑟 = = −2𝐷 −0.5  Spectroscopy The science of spectroscopy grew out of studies of the interaction of electromagnetic energy with matter. When light shines on an object, for example, we know that part of the light is scattered (reflected) and part is absorbed. Of the initial part that is absorbed, some is later emitted as light of a different color or wavelength.  What is spectroscopy Spectroscopy is the study of the absorption and emission of light and other radiation by matter. It involves the splitting of light (or more precisely electromagnetic radiation) into its constituent wavelengths (a spectrum), which is done in much the same way as a prism splits light into a rainbow of colours. In fact, old style spectroscopy was carried out using a prism and photographic plate. Optical instruments called spectrometers reveal in photographic or printed records as a series of specific wavelengths or frequencies of the light energies absorbed and emitted. These records, in turn is referred to as spectra.  SPECTROMETER Spectrometer is a device used for detecting and analyzing wavelengths of electromagnetic radiation  TYPES OF SPECTROMETER NMR Spectrometer The NMR spectrometer observes and measures the interaction of nuclei spins when the sample is placed in a strong, constant magnetic field Mass Spectrometer A mass spectrometer measures the mass-to-charge ratio of ions and identifies the composition of elements present in a sample. Optical Spectrometer An optical spectrometer measures the properties of light, usually near the optical region in the electromagnetic spectrum, i.e. ultraviolet, visible and infrared light ESSENTIAL COMPONENTS OF A SPECTROMETER A spectrometer consists of three main components: entrance slit grating detector USES OF A SPECTROMETER Optical spectrometers have a wide range of applications across physics, chemistry, and biology. You can use them to measure the transmission, reflection, scattering, or absorption of light on a sample as well as electroluminescence or photoluminescence from an emitter.