Choose true/false according to given sentences:

The angle subtended at the eye by an object is equal to the angle subtended at the eye by the virtual image produced by a magnifying glass. In viewing through a magnifying glass, one usually positions one's eyes very close to the lens. Magnifying power of a simple microscope is inversely proportional to the focal length of the lens.

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True

False

answer is A.

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Detailed Solution

The given statement is true.
Concept- Angle magnification: When using magnifiers or binoculars, the angle magnification is proportional to the ratio of the tangents of the angles formed by the target and its reflection as measured from a certain position in the instrument.
Magnifying power: The geometry of the optical device is related to the magnifying force or the extent to which the object is visible, and the field of vision or the heights of the object that can be seen.
The angular size of the picture is equal to the angular size of the item, despite the image's larger size than the thing. A magnifying glass enables clear viewing of things that are closer than their minimum width. An item that is nearer has a larger angular measurement. An optical magnifier ensures angular magnification. Without magnification, it is impossible to place the item close to the eye. With magnification, the item may be placed much closer to the eye.
The angular magnification does indeed change. The amount of angular magnification drastically reduces when the distance between the eye and the magnifying glass is increased. Because the angle beneath the eye is only a little bit less than the angle beneath the mirror, this occurs. Angled magnification is not significantly affected by image distance.
A convex lens' focal length cannot be reduced by a bigger margin. This is because making lenses with very small focus lengths is not practical. chromatic and spherical aberrations brought on by a convex lens's extremely short focal length.
The angular magnification produced by the eyepiece of a compound microscope is
Question Image

, where

is the focal length of the eyepiece.
It can be assumed that if the focal length of the eyepiece is small, the angular magnification of the eyepiece would be high.
The angular magnification of the objective lens of the compound microscope is as:

Where,

is the object distance of the objective lens

is the focal length of the objective
When

The object is near the objective lens and the magnification is great.
The item is therefore quite close in distance. Given the close proximity of the item, the focus length would be considerably shorter. Therefore, the focal length of the eyepiece and the object are both shorter.
The item is therefore quite close in distance. Given the close proximity of the item, the focus length would be considerably shorter. Therefore, the focal length of the eyepiece and the object are both shorter.
We can't collect a lot of refracted light when we put our eyes too close to the compound microscope's eyepiece. As a result, the field of view is greatly reduced. As a result, the picture's clarity is compromised.
E) The eye is optimally positioned at the eye-ring attached to the eyepiece for inspection through a compound magnifying lens. The distance between the eyepiece and the target focus point determines the exact location of the eye.
Hence, the given statement is true.

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