Optical Instrument, Microscope

A Microscope consists of an objective lens and an ocular lens (eyepiece lens). Both of them are positive lens. The focal length of the objective lens is less than the focal length of the ocular lens. The object is placed a little further than it focus. The final image resulted by the ocular lens is inverted and virtual.

Angle magnification for objective lens

Where :
Mob = angle magnification of objective lens
fob = focal length of the objective lens
S’ob = the distance of objective’s image from the objective lens
Sob = the distance of the objective’s object from the objective lens

Angle magnification for the ocular lens

Angle magnification of the ocular lens similar to that for the magnifying glass. Basically the ocular lens functions just as the magnifying glass.

If the ocular’s image located at the near point then

If the ocular’s image located at the far point (for normal eyes) then

If the ocular’s image located at a distance x between the near point and far point then

The total magnification of the microscope is

The distance of the ocular object in front of the ocular lens is given by

Wherever the ocular’s image located. The length of the microscope cylinder is

Optical Instrument, Magnifying Glass

To see a small object. Object observed with a magnifying glass seems bigger. The magnifying power is the ratio between the angle of the eyes observing the image of the object using the magnifying glass and the angle of the eyes directly observing the object with maximum accomodation.

The magnification power :

where Sn is the near point ( typically 25 cm), d is the distance between the eyes and the glass.

For d = 0

maximum magnification is obtained when the image is at the near point,

the angular magnification become :

minimum magnification is obtained when the image is at the far point, then

the angular magnification become :

If the image is laid between the near point and far point then

the angular magnification become :

Note : for myopia eyes, when the image is at the far point, then

The distance of the object from the lens can be determined by the formula

Optical Instrument , The Eye and Glasses

Human beings typically have a capability to see ranging about 25 cm to infinity. 25 cm is usually called as near point (punctum proximum ) and infinity is the far point (punctum remotum).

When one reads, he will put the reading about 25 cm to be able to read clearly. At this time the eyes’ lens are thickened to focus the near object to the retina. We called the eyes in its maximum accomodation. One whose near point further than 25 cm is called hyperopia. In order to read an object at the normal distance, he can be helped by spectacles with positive lens.

Without the lens, the image of the object at 25 cm will falls behind the retina.

Applying lens to the eyes can help the them to focus the object to the retina.

The measure of the power of the lens can be determined as follow

Where P is the power of the lens expressed in diopter , PP is the punctum proximum in cm.

In order to see a distant object, one will set his eyes’ lens thin to focus it onto his retina. But in some cases, one fails to do that. This kind of eyes in called myopia.The image of the object falls in front of the retina.

This eyes can be helped using a negative lens.

The power of the lens needed can be determined as follow

P is the power of the glasses’ lens, PR is the punctum remotum (far point), that is maximum distance of an object that still can be seen by the man.

The image of the object for glasses always virtual, so S’ has negative values.

In general, we can summarize the formula of the power of the lens with

Where P is the power of the lens, x is the preferred distance to see, PP or PR is the punctum proximum (near point) and punctum remotum (far point) respectively.

Rumus Fisika UN 2009 according to SKL

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