Optical Instruments - Corrective Lenses

Introduction

Web Lecture

Optical Instruments

The camera

The camera's purpose is to focus light on film in order to capture a picture. It does this by allowing the user to control

• Shutter speed (faster = less light gets to the film)
• Size of the diaphragm opening. The ratio of the diaphragm to the focal length of the lens f/D is called the f-stop. "Stopping down" from f/16 to f/32 means that the diaphragm gets smaller and lets in less light.
• Focus, by moving the lens with relation to the film to vary the image distance. Using 1/f = 1/d_o + 1/d_i, we can determine how much the image distance d_i must change in order to compensate for objects at different d_o distances.

Corrective lenses for the human eye

The human eye is itself a lens. The cornea refracts all the light coming into the eye, getting most of it "close" to focus. The lens then takes over, flattening or bulging in response to pulls from the ciliary muscles, and finishes the job of focusing the light on the retina at the rear of the eyeball. The iris opens or closes the pupil, controlling the amount of light coming into the eye and keeping it at safe levels.

If the eyeball is too long (from use or from genetic tendencies), the individual will experience myopia or nearsightedness, where the light is focused inside the eyeball.. If the eyeball is too short, the individual will be hyperopic, and the focused image point will lie beyond the retina. If the individual suffers from presbyopia, he or she will not be able to flex the lens enough to shorten the image distance for close objects, and will be effectively farsighted.

If the retinal surface is not smoothly curved, but has wrinkles or is warped, then the image will not be in focus throughout. Some areas will be sharp while others are fuzzy or lighter in color.

In order to correct the defects in human eyes, optometrists create lenses--glasses and contacts) which focus the incoming light enough that the eye can finish the job. Most exercises in glasses involve using the lens formula to determine how to create the artificial lens that will place an appropriate image on the organic lens.

Magnifying glasses

A magnifying glass is a simple lens which also follows the lens formula: $$\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$$

For human vision, we can consider the image at the near point N (about 25cm) as the image distance:

Rewriting the lens formula, we have: $$\frac{1}{d_o}=\frac{1}{f}-\frac{1}{d_i}=\frac{1}{f}+\frac{1}{N}$$

Now we can determine the magnification appropriate to human eye lenses: $$\begin{array}{l}M=-\frac{d_i}{d_o}=\frac{N}{d_o}=N(\frac{1}{f}+\frac{1}{N})\\ M=\frac{N}{f}+\frac{N}{N}=\frac{N}{f}+1\end{array}$$

Lensmakers use this relationship in crafting eyeglasses.

Practice with the Concepts

Discussion Points

• Why is the depth of field greater, and the image sharper, when a camera lens is “stopped down” to a larger f-number? Ignore diffraction. horizontal to obtain best reception?
• In attempting to discern distant details, people will some- times squint. Why does this help?

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