W9_parallel_resonance.eps

408 Week 12: Lenses and Mirrors

12.6: Optical Instruments

The Simple Magnifier

The “size” of an object to the human eye is determined by three distinct things. Humans

have binocular vision, and useparallax– the apparent displacement of an object seen from

two slightly different positions – to get a sense of an object’s distance. This is reinforced

by the physiological sense ofaccommodation, which gives one a sense of relative nearness.

Finally, given the distance, it is determined by theanglethe image subtends on the retina.

x

f

np

β

y α

y

Figure 171: A converging lens used as a simple magnifier.

To see a small thing as clearly as possible, we naturally bring it to the closest point

we can, so its details subtend the largest possible angle when our eyes are maximally

accommodating. In figure (171) the top picture shows an object of heightyviewed at

the near point. When the image is focused on the retina by the maximally accomodating

eye, it subtends an angle ofα, where:

α≈tan(α) =

y

xnp (998)

in the small angle approximation (which is entirely justified because weonly “see” detail

with the macula, which in turn only occupies around 0.2 radians in the center of the

visual field. Even if we are examining a larger object, we do so by redirecting the eye to

look at it in patches that cover it in small angle chunks.

To use a simple magnifier we place a converging (f >0) lens immediately in front of the

eye. The object is placed at its focal point. It therefore forms avirtual imageat−∞

that is automatically brought into focus by the relaxed normal (or vision corrected) eye.

It now subtends an angleβon the retina given by:

β≈tan(β) =

y

f

(999)

The magnification is therefore the ratio of the new angle (with the magnifier) to the

angle without it, when the object is seen at the near point. The magnification of the

object occurs because one can bring the objectcloserto the eye thanxnpand still see it

clearly (more clearly, even, than before given that one does not have to accommodate).

Its magnification is given by:

M=

β

α

=

xnp

f

(1000)

It is very important to understand the simple magnifier, as it forms the eyepiece ofboth

the microscopeandthe telescope, our next two optical instruments.