Lecture Outlines Chapter 27 Physics, 3rd Edition James S. Walker © 2007 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials.

Chapter 27 Optical Instruments

Units of Chapter 27 The Human Eye and the Camera Lenses in Combination and Corrective Optics The Magnifying Glass The Compound Microscope Telescopes Lens Aberrations

27-1 The Human Eye and the Camera Light passes through the cornea of the human eye and is focused by the lens on the retina. The ciliary muscles change the shape of the lens, so it can focus at different distances. The vitreous and aqueous humors are transparent. Rods and cones on the retina convert the light into electrical impulses, which travel down the optic nerve to the brain.

27-1 The Human Eye and the Camera The eye produces a real, inverted image on the retina. Why don’t things look upside down to us? The brain adjusts the image to appear properly.

27-1 The Human Eye and the Camera The ciliary muscles adjust the shape of the lens to accommodate near and far vision.

27-1 The Human Eye and the Camera The near point is the closest point to the eye that the lens is able to focus. For those with normal vision, it is about 25 cm from the eye, but increases with age as the lens becomes less flexible. The far point is the farthest point at which the eye can focus; it is infinitely far away, if vision is normal.

27-1 The Human Eye and the Camera The simplest camera consists of a lens and film in a light-tight box:

27-1 The Human Eye and the Camera The camera lens cannot change shape; it moves closer to or farther away from the film in order to focus. The f-number characterizes the size of the aperture: The combination of f-number and shutter speed determines the amount of light that reaches the film.

27-2 Lenses in Combination and Corrective Optics In a two-lens system, the image produced by the first lens serves as the object for the second lens.

27-2 Lenses in Combination and Corrective Optics To find the image formed by a combination of lenses, consider each lens in turn, starting with the one closest to the object. The total magnification is the product of the magnifications of each lens.

27-2 Lenses in Combination and Corrective Optics A nearsighted person has a far point that is a finite distance away; objects farther away will appear blurry. This is due to the lens focusing too strongly, so the image is formed in front of the retina.

27-2 Lenses in Combination and Corrective Optics To correct this, a diverging lens is used. Its focal length is such that a distant object forms an image at the far point:

27-2 Lenses in Combination and Corrective Optics The strength of corrective lenses is usually quoted as refractive power, which is the inverse of the focal length:

27-2 Lenses in Combination and Corrective Optics A person who is farsighted can see distant objects clearly, but cannot focus on close objects – the near point is too far away. The lens of the eye is not strong enough, and the image focus is behind the retina.

27-2 Lenses in Combination and Corrective Optics To correct farsightedness, a converging lens is used to augment the converging power of the eye. The final image is past the near point:

27-3 The Magnifying Glass A magnifying glass is a simple convex lens. Working in conjunction with the eye, it makes objects appear bigger because it makes them appear closer. Similar to a corrective lens for farsightedness, it brings the near point closer to the eye.

27-3 The Magnifying Glass The angular size of an object is the angle it subtends on the retina, and depends both on the size of the object and its distance from the eye.

27-3 The Magnifying Glass This angle, assuming it is small, is given by the height of the object divided by its distance from the eye. If the object is moved closer to the eye, its angular size increases. If it is placed at the near point, its size is:

27-3 The Magnifying Glass Now, place a converging lens whose focal length is less than N very close to the eye, and place the object at the focal point of the lens. This gives the object a larger angular size.

27-3 The Magnifying Glass The angular magnification is then given by:

27-3 The Magnifying Glass The magnification can be maximized by having the image at the near point:

27-4 The Compound Microscope A compound microscope has, in its simplest form, two converging lenses. One, the eyepiece, is close to the eye, while the objective is close to the object.

27-4 The Compound Microscope The object is placed near the focal point of the objective lens, giving a magnification of: The image formed is at the focal point of the eyepiece, which produces an image at infinity:

27-4 The Compound Microscope The total magnification is given above, and is the product of the magnification of each lens.

27-5 Telescopes Telescopes are similar to microscopes in that they have an objective and an eyepiece. However, the objects observed are essentially at infinity, so the light will be focused at the focal point of the objective. The objects themselves are very large, but their angular size is very small due to their great distance.

27-5 Telescopes The image formed by the objective is at the focal point of the eyepiece.

27-5 Telescopes The total magnification of the telescope is the product of the magnification of each lens, and is: Telescopes using lenses are called refractors; the first telescopes made were of this type.

27-5 Telescopes It is desirable to have the objective of a telescope be as large as possible, so that it may collect as much light as possible. Each doubling of the diameter of the objective gives four times as much light. Very large lenses are difficult to handle; they are thick and heavy, must have two precision surfaces, and absorb more of the light the thicker they are.

27-5 Telescopes Therefore, large telescopes are now made as reflectors – the objective is a mirror rather than a lens. The mirror has only one surface, can be made very thin, and reflects almost all the light that hits it.

27-6 Lens Aberrations Spherical aberration occurs when light striking the lens far from the axis does not focus properly. It can be fixed by grinding the lens to a precision, non-spherical shape.

27-6 Lens Aberrations Chromatic aberration occurs when different colors of light focus at different points.

27-6 Lens Aberrations Chromatic aberration can be improved by combining two or more lenses that tend to cancel each other’s aberrations. This only works perfectly for a single wavelength, however.

Summary of Chapter 27 The human eye is focused by the ciliary muscles, which change the shape of the lens. A camera is focused by changing the distance from the lens to the film. The near point is the closest point at which the eye can focus, typically 25 cm. The far point is the farthest point at which the eye can focus, typically at infinity. f-number of a lens:

Summary of Chapter 27 In lens combinations, the image formed by one lens serves as the object for the next. Nearsightedness occurs when the image is focused in front of the retina, causing the far point to be closer than infinity. It can be corrected with a diverging lens. Farsightedness occurs when the image is focused behind the retina, causing the near point to be more than 25 cm from the eye. It can be corrected by a converging lens.

Summary of Chapter 27 Refractive power of a lens in diopters, when the focal length is in meters: A magnifying glass is a converging lens. Its magnification is given by:

Summary of Chapter 27 A compound microscope uses two lenses, the objective and the eyepiece, to form an image of a small object placed close to the focal point of the objective. Its magnification is given by:

Summary of Chapter 27 A refracting telescope also uses two lenses to form an image of a very distant object. Its magnification is given by: The length of the telescope will be: A telescope having a mirror instead of a lens as the objective is called a reflecting telescope.

Summary of Chapter 27 Lens aberrations can distort images. Spherical aberration occurs because off-axis rays do not focus at the focal point. It can be corrected by precision shaping of the lens. Chromatic aberration occurs because different frequencies of light have different indices of refraction. It can be corrected by using multiple lenses in an achromatic lens system.