Physics 1CLecture 25B

"More than 50 years ago, Austrian researcher Ivo Kohler gave people goggles thats severely distorted their vision: The lenses turned the world upside down. After

several weeks, subjects adjusted--their vision was still tweaked, but their brains were processing the images so they'd appear normal. In fact, when people took the

glasses off at the end of the trial, everything seemed to move and distort in the opposite way."

--Sunny Bains

Simple MagnifierProbably the simplest optical system is a single converging lens which is also called a simple magnifier.This will magnify the image compared to the original object.When the object is placed just in front of the focal point of a converging lens, the lens forms a virtual, upright, and enlarged image.

Simple MagnifierAngular magnification is defined as:The angular magnification is at a maximum when the image formed by the lens is at the near point of the eye (q = -25cm).The thin-lens equation becomes:

Simple MagnifierSolving for the image distance, p, gives:

For the max case, the object distance merely depends on f.

Simple MagnifierThe normal eye can focus on anything placed between the near point and infinity.Since the near point for normal vision is 25cm (for max case):

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θo ≈h

25 cmAnd since the object is at the focal point:

Note in this max case that the angles θ and θo are small (<20o).

Simple MagnifierBecause these angles are so small we can make the small angle approximation:

The max magnification becomes:

Simple MagnifierCanceling out the 25cm gives us:

With a single converging lens, it is possible to achieve angular magnification up to about 4 without serious aberrations.With multiple lenses, magnifications of up to about 20 can be achieved.

Compound MicroscopeA compound microscope consists of two lenses separated by a distance L.It gives greater magnification than a single lens.The lens closest to the object is labeled the objective lens and the lens closest to the eye is labeled the eyepiece.The objective lens has a short focal length to produce a real image.

Compound MicroscopeThe goal is to place the image from the objective lens just inside the near focal point for the eyepiece.This creates a final virtual image that is inverted and very much enlarged compared to the original object.

You will use the same approach for this as you did two lens systems.

Compound MicroscopeThe magnification of the objective lens will be given by (also called the lateral magnification), Ml, is:

The magnification of the eyepiece will work as a simple magnifier such that:

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Ml = −q1p1

= −L − fefo

≈ −Lfo

€

me =θθο

≈25 cmfe

Compound MicroscopeThus, the overall magnification given by the microscope of the original object will be:

The ability of an optical microscope to view an object depends on the size of the object relative to the wavelength of light used to observe it.

€

mtot = me ⋅ Ml =25 cmfe

⎛

⎝ ⎜

⎞

⎠ ⎟ −

L − fefo

⎛

⎝ ⎜

⎞

⎠ ⎟ ≈

25 cmfe

⎛

⎝ ⎜

⎞

⎠ ⎟ −

Lfo

⎛

⎝ ⎜

⎞

⎠ ⎟

Telescopes

2) Reflection: Those telescopes that use a curved mirror and a lens to form an image.Whichever type they are, they still use the basic principle that the image of the first optical element becomes the object of the second optical element.

There are many varieties of telescopes but they can be broken down into two types:1) Refraction: Those telescopes that use combinations of lenses to form an image.

TelescopesFor refracting telescopes, the two lenses are oriented such that the objective lens forms a real, inverted image of a very distant object

This image will be very close to the focal point of the eyepiece.The length of the telescope tube will essentially be the addition of the two focal lengths:

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L ≈ fo + fe

TelescopesThe eyepiece will then form a virtual image of this object.

It will be enlarged and inverted compared to the original object.The angular magnification will be given by:

TelescopesFor reflecting telescopes, mirrors reflect light so that they may be viewed by the observer.

To the right is a Newtonian telescope, the incoming rays are reflected from the mirror and converge toward point A.A small flat mirror, M, reflects the light toward an opening in the side and passes into an eyepiece.

ResolutionThe ability of an optical system to distinguish between closely spaced objects is limited due to the wave nature of light.If two sources of light are close together, they can be treated as non-coherent sources.Since we are looking through an opening, diffraction can occur where the images consist of bright central regions flanked by weaker bright and dark rings.If the two sources are separated so that their central maxima do not overlap, their images are said to be resolved.

ResolutionThe limiting condition for resolution is called Rayleigh’s Criterion:

When the central maximum of one image falls on the first minimum of another image, the images are said to be just resolved.The images are just resolved if their angular separation satisfies Rayleigh’s criterion.

ResolutionIf viewed through a slit of width, a, and applying Rayleigh’s criterion, the limiting angle of resolution is:

For the images to be resolved, the angle subtended by the two sources at the slit must be greater than θmin.For a circular opening of diameter D:

Clicker Question 25B-1Two campers wish to start a fire during the day. One camper is nearsighted and one is farsighted. Whose glasses should be used to focus the Sun’s rays onto to some paper to start the fire?

A) The nearsighted camper.

B) The farsighted camper.

C) Either camper.

D) Neither camper.

Clicker Question 25B-2For a person with normal vision their near and far points will most likely be:

A) 5 centimeters and infinity, respectively.

B) 1 meter and infinity, respectively.

C) 25 centimeters and infinity, respectively.

D) 5 centimeters and 1 meter, respectively.

E) 1 meter and 100 meters, respectively.

For Next Time (FNT)

Keep reading Chapter 25

Start working on the homework for Chapter 24