doPhysics · Optics
Optical Instruments and the Eye
How the eye focuses and why it sees size as an angle, the defects of vision and their spectacles, the simple and compound microscope, and the refracting and reflecting telescope, each with its magnifying power.
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Why this chapter
Why this chapter exists
Every image you have ever seen was formed by a lens: the one in your own eye. This chapter starts there. The eye focuses by changing the power of its lens, and it judges size by the angle an object makes. When the eye's lens is too strong, too weak or too stiff, a spectacle lens of the right power in dioptres puts things right. A single convex lens then lets an object come closer than the eye allows. Two lenses make a compound microscope, which shows an onion cell as a brick. Two lenses of another kind, or a pair of mirrors, make a telescope, which brings the Moon within reach.
You will learn
By the end of this chapter you will
- Describe the parts of the eye, and explain accommodation, the near point and the far point with a one-lens model of the eye.
- Explain why the apparent size of an object is the angle it makes at the eye, and define magnifying power as a ratio of angles.
- Find the lenses that correct myopia, hypermetropia and presbyopia, and explain astigmatism and the cylindrical lens.
- Derive and use \(M = 1 + D/f\) and \(M = D/f\) for a simple microscope, and explain why it stops at about ten times.
- Find the magnifying power \(m_oM_e\) and the tube length of a compound microscope, with the image at \(D\) and at infinity.
- Find the magnifying power and length of an astronomical telescope, and explain the erecting lens, binoculars and the Cassegrain reflector.
Before you begin
Before you begin
From the chapter on Spherical Surfaces and Lenses, you should know the lens formula \(1/v - 1/u = 1/f\) and the magnification \(m = v/u\). You should also know the power of a lens in dioptres and the three easy rays. From the chapter on Reflection, you should know how a concave and a convex mirror form images. You should be comfortable with the Cartesian sign convention and with small angles in radians.
Lessons
1
The Eye and How It Focuses
The parts of the eye and the real, inverted image on the retina. How the eye lens changes its power to focus near and far objects, the near point and the far point, and why the apparent size of an object is the angle it makes at the eye.
The eye as a cameraAccommodation near point and far pointApparent size is an angle
2
Defects of Vision and Spectacles
Myopia and its concave lens, hypermetropia and its convex lens, presbyopia and bifocals, and astigmatism and the cylindrical lens. Every correcting lens does one job, placing a virtual image where the eye can see.
MyopiaHypermetropiaPresbyopia and bifocalsAstigmatism
3
The Simple Microscope
A convex lens held close to the eye lets an object come inside the near point and still be seen sharp. Its magnifying power is 1 + D/f with the image at D and D/f with the image at infinity, and aberrations stop a single lens at about ten times.
The magnifying glassMagnifying power at the near point and at infinityWhy a simple microscope stops at ten
4
The Compound Microscope
Two convex lenses share the work. The objective forms a real, inverted, enlarged image, and the eyepiece views it as a magnifying glass. The magnifying power \(m_o \times M_e\), the tube length for the image at \(D\) and at infinity, and why the objective has a very short focal length.
Objective and eyepieceMagnifying power of a compound microscopeNormal adjustment and tube length
5
Telescopes
The astronomical telescope and its magnifying power \(f_o/f_e\) and length \(f_o + f_e\) in normal adjustment, the image at \(D\), the terrestrial telescope with its erecting lens and binoculars with their prisms, and the reflecting telescope with the Cassegrain arrangement.
The astronomical telescopeThe terrestrial telescope and binocularsReflecting telescopes
Read in order. The small labels are the topics of each lesson. They take your colour as you answer the checks.
0%The Workbook
Questions to solve on paper, marked by you.
Glossary
The key words of this chapter, with the meaning this chapter gives them.
- accommodation
- The ability of the eye to change the power of its lens, so that objects at different distances form sharp images on the retina.
- astigmatism
- A defect in which the cornea is curved more in one plane than in the plane at right angles, so lines in one direction blur. A cylindrical lens corrects it.
- astronomical telescope
- A telescope of two convex lenses, an objective of long focal length and an eyepiece of short focal length. It gives an inverted image, with \(M = f_o/f_e\) in normal adjustment.
- bifocal lens
- A spectacle lens with two powers: the upper part for distant objects and the lower part for reading.
- binoculars
- A pair of short telescopes, one for each eye. In each, two right-angled prisms fold the light path by total internal reflection and turn the image upright.
- Cassegrain telescope
- A reflecting telescope with a concave primary mirror and a small convex secondary. The secondary sends the light back through a hole in the primary to the eyepiece.
- ciliary muscles
- The ring of muscles that holds the eye lens. Relaxed, they keep the lens thin for distant objects; contracted, they let it bulge for near ones.
- compound microscope
- A microscope of two convex lenses. The objective forms a real, enlarged image, and the eyepiece views it as a magnifying glass.
- cornea
- The clear, curved front window of the eye. Light meets the largest change of refractive index there, so the cornea does most of the eye's bending.
- cylindrical lens
- A lens with one face shaped like part of a cylinder. It bends light in the plane across its axis only, and is used to correct astigmatism.
- erecting lens
- A convex lens placed so that the objective's image is at twice its focal length. It forms an upright image of the same size, and adds four times its focal length to the length of the telescope.
- eye lens
- The soft, clear lens behind the pupil. Its shape, and so its power, changes to focus objects at different distances.
- eyepiece
- The lens of an instrument next to the eye. It views the image formed by the objective as a magnifying glass.
- far point
- The farthest point that the relaxed eye can see clearly. For a normal eye it is at infinity.
- hypermetropia
- Long sight. The eye is too weak for its length, so near objects focus behind the retina and the near point is beyond \(25\,\text{cm}\). A convex lens corrects it.
- least distance of distinct vision
- The distance \(D\) of the near point of a normal eye, taken as \(25\,\text{cm}\). It is the reference distance for the magnifying power of a microscope.
- magnifying power
- The ratio \(M = \beta/\alpha\) of the angle the final image makes at the eye to the angle the object makes at the unaided eye. It is also called the angular magnification.
- myopia
- Short sight. The relaxed eye is too strong for its length, so distant objects focus in front of the retina and the far point is near. A concave lens corrects it.
- near point
- The nearest point that the eye can see clearly with its greatest accommodation. For a normal young eye it is about \(25\,\text{cm}\) away.
- normal adjustment
- The setting of a microscope or telescope in which the final image is at infinity, so that the eye views it relaxed.
- objective
- The lens or mirror of an instrument that faces the object and forms the first image. In a microscope it has a very short focal length; in a telescope a long one.
- presbyopia
- The loss of accommodation with age, as the eye lens stiffens and the ciliary muscles weaken. The near point recedes, and a convex reading lens or a bifocal corrects it.
- pupil
- The round opening in the middle of the coloured iris. The iris narrows it in bright light and widens it in dim light.
- reflecting telescope
- A telescope whose objective is a concave mirror. It has no chromatic aberration and can be made very large.
- retina
- The thin layer of light-sensitive cells at the back of the eye, on which the eye forms a real, inverted image.
- simple microscope
- A convex lens held close to the eye with the object inside its focus. It forms an erect, enlarged, virtual image; also called a magnifying glass.
- terrestrial telescope
- A telescope for use on land, with an erecting lens between the objective and the eyepiece, so that the final image is upright.
- tube length
- In this book, the distance between the objective and the eyepiece of a microscope, \(L = v_o + |u_e|\).
- visual angle
- The angle that an object makes at the eye, about \(h/d\) for a small object of height \(h\) at distance \(d\). It sets the size of the image on the retina, and so the apparent size.