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 The eye produces a real, inverted image on the retina. Why don’t things look upside down to us?
The two eyes produce each a real, inverted image on the retina. Why don’t we see two images?
The ciliary muscles adjust the shape of the lens to accommodate near and far vision.
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.
Problem 27-3: Approximating the eye as a single thin lens 1.95 cm from the retina, find the eye's near-point distance if its focal length is 1.61 cm when focused at infinity. Answer: 9.23 cm
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 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:
Without his glasses, Isaac can see objects clearly only if they are less than 6.0 m (di+D) from his eyes. What focal length glasses worn 2.0 cm from his eyes will allow Isaac to see distant objects clearly? Answer: -5.98 m do di D
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:
Problem 27-48: A beetle 7.44 mm long is examined with a simple magnifier of focal length f = 11.0 cm. If the observer's eye is relaxed while using the magnifier and has a near-point distance of 25 cm, what is the apparent length of the beetle?asnwer: 16.9 mm
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.