Question

Answer the following questions:
A) 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 what sense then does a magnifying glass provide angular magnification?
B) In viewing through a magnifying glass, one usually positions one's eyes very close to the lens. Does angular magnification change if the eye is moved back?
C) Magnifying power of a simple microscope is inversely proportional to the focal length of the lens. What then stops us from using a complex lens of smaller and smaller focal length and achieving greater and greater magnifying power?
D) Why must both the objective and eyepiece of a compound microscope have short focal lengths?
E) When viewing through a compound microscope, our eyes should be positioned not on the eyepiece but a short distance away from it for best viewing, Why? How much should be that short distance between the eye and the eyepiece?

Answer 1

Hint: Angular magnification: Angular magnification is proportional to the ratio of the tangents of the angles undercut by the target and its reflection as measured from a given point in the instrument, as with magnifiers and binoculars.
Magnifying power:
The magnifying force or the degree to which the object is seen is expanded and the field of vision or the heights of the object that can be seen are connected to the geometry of the optical device.

Complete step-by-step answer:
A) While the size of the image is greater than the object, the angular size of the image is equal to the angular size of the object. A magnifying glass allows one to see objects that are closer than the least width with a distinct vision. A closer object has a greater angular measurement. A magnifying glass guarantees angular magnification. The object cannot be positioned near the eye without magnification. The object may be positioned far closer to the eye with magnification.
B) Yes, the angular magnification changes. As the distance between the eye and the magnifying glass is raised, the angular magnification decreases significantly. This is because the angle beneath the eye is marginally smaller than the angle underneath the mirror. Image distance has little effect on angular magnification.
C) The focal length of a convex lens cannot be shortened by a larger amount. This is because it is not convenient to produce lenses of very short focal lengths. Spherical and chromatic aberrations caused by a convex lens with a very short focal length.
D) The angular magnification produced by the eyepiece of a compound microscope is
$\left( {\dfrac{{25}}{{{f_e}}}} \right) + 1$, where ${f_e}$ 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:
$\dfrac{1}{{{\mu _ \circ } \times {f_ \circ }}}$
Where, ${\mu _ \circ }$ is the object distance of the objective lens
${f_ \circ }$ is the focal length of the objective
When ${\mu _ \circ } > {f_ \circ }$, the magnification is high and the object is close to the objective lens.
The distance of the object is thus very small. As the object distance is small, the focal length would be even smaller. So, both the object focal length and eyepiece focal length is smaller.
At the point when we place our eyes excessively near the eyepiece of a compound microscope, we can't gather a lot of refracted light. Thus, the field of view diminishes generously. Consequently, the clearness of the picture gets obscured.
E) The best situation of the eye for survey through a compound magnifying lens is at the eye-ring connected to the eyepiece. The exact area of the eye relies upon the partition between the target focal point and the eyepiece.

Note: Here we have to pay attention as to where the eyepiece along with the focal length and object is situated.
A compound microscope is used for viewing many magnified objects.