Least Distance of Distinct Vision

The minimum distance from the eye at which an object appears to be distinct is called the least distance of distinct vision or near point.  

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      The normal human eye can focus a sharp image of an object on the eye if the object located any where from infinity to a certain point called the "Near Point".

The minimum distance of an object from eye to have its clear image is called "Least Distance of Distinct Vision".

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     This distance is about 25 cm from the eye. It is denoted by d. If the object is held closer to the eye than this distance the image formed will be blurred and fuzzy. The location of the near point, however, changes with age.

Visual Angle

The angle subtended by an object at the retina of eye in called "Visual Angle". The apparent size of an object depends upon its actual size and on the angle subtended by it at the eye.Thus the closer the object is to the eye, the greater is the angle subtended and larger appears the size of the object.

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The greater the visual angle, the greater is the apparent size of the object.

Object Angle

       When the object is displaced at d, then the angle subtended at a naked (unaided) eye, by the object is called the "Object Angle". It is denoted by (alpha).

 Ray diagram for Object Angle

Image Angle

        When the angle subtended by the image, formed at d, on the naked eye, is called "Image angle". It is denoted by (beta).

Ray diagram for Image Angle

Linear Magnification

       The ratio of the size of the image to the size of the object is called "Magnification". It is denoted by M.

where,

                      I = Image Size

                      O = Object Size

p = Distance of object from the lens or mirror

q = Distance of image from the lens or mirror

Derivation for the Above Equation
        When an object is placed in front of a convex lens at a point beyond its focus, a real and inverted image of the object is formed as shown in the figure:

From the above figure, ∆ABO and ∆A'B'O are similar triangles.

       For similar triangles the ratio of the length of the corresponding sides is equal i.e,

Since

OB' = q = Image Distance

OB = p = Object Distance

Therefore,

As,

Therefore,

Angular Magnification

      The ratio of the angles subtended by the image as seen through the optical device (aided eye) to that subtended by the object at the naked (unaided) eye, is called "Angular Magnification". It is also called the magnifying power, Mathematically,