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 convex lens of smaller and smaller focal length and achieving greater and greater magnifying power? (d) Why must both the objective and the 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 eyepiece?
a)
Even though the size of the virtual image that is produced by a magnifying glass is bigger than the actual object, the angular size of the image is equal to the angular size of the object. A magnifying glass helps to see the objects placed closer than the least distance of distinct vision ( 25 cm ). The closer the object is to the eye, the larger is its angular size. A magnifying glass provides angular magnification. With magnification, the object can be placed much closer to the eye.
b)
When the distance between the eye and a magnifying glass is increased, the angle subtended at the eye by the object becomes slightly less than the angle subtended by it at the lens. So, the angular magnification decreases a little. Image distance does not have any effect on angular magnification.
c)
The focal length of a convex lens cannot be decreased by a great amount to increase the magnifying power. This is because making lenses with very small focal lengths is a complex task. Moreover, the convex lenses having small focal length produce spherical and chromatic aberrations.
d)
The angular magnification produced by the eyepiece of a compound microscope is given as,
α e = [ ( 25 f e ) + 1 ]
Where, f e is the focal length of the eyepiece.
Thus, the smaller the focal length of the eyepiece, the greater the magnification produced.
The angular magnification produced by the objective of a compound microscope is given as,
α o = 1 ( | u 0 | f 0 )
Where, u 0 is the object distance for the objective lens and f 0 is focal length of the objective lens.
Thus, the smaller the focal length of the objective, the greater the magnification produced.
The magnification is large when u o > f o . In the case of a microscope, the object is kept closer to the objective lens. Hence, the object distance is very little. Since u o is small, f o will be even smaller. Therefore, f e and f o are both small in the given condition.
e)
We are unable to collect much refracted light when we place our eyes very close to the eyepiece of a compound microscope. As a result, there is substantial decrement in the field of view. Hence, the clarity of the image gets blurred. The eye-ring attached to the eyepiece gives the best position for viewing through a compound microscope. The precise location of the eye depends on the separation between the objective lens and the eyepiece.
Thus, 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.
a)
Even though the size of the virtual image that is produced by a magnifying glass is bigger than the actual object, the angular size of the image is equal to the angular size of the object. A magnifying glass helps to see the objects placed closer than the least distance of distinct vision (
b)
When the distance between the eye and a magnifying glass is increased, the angle subtended at the eye by the object becomes slightly less than the angle subtended by it at the lens. So, the angular magnification decreases a little. Image distance does not have any effect on angular magnification.
c)
The focal length of a convex lens cannot be decreased by a great amount to increase the magnifying power. This is because making lenses with very small focal lengths is a complex task. Moreover, the convex lenses having small focal length produce spherical and chromatic aberrations.
d)
The angular magnification produced by the eyepiece of a compound microscope is given as,
Where,
Thus, the smaller the focal length of the eyepiece, the greater the magnification produced.
The angular magnification produced by the objective of a compound microscope is given as,
Where,
Thus, the smaller the focal length of the objective, the greater the magnification produced.
The magnification is large when
e)
We are unable to collect much refracted light when we place our eyes very close to the eyepiece of a compound microscope. As a result, there is substantial decrement in the field of view. Hence, the clarity of the image gets blurred. The eye-ring attached to the eyepiece gives the best position for viewing through a compound microscope. The precise location of the eye depends on the separation between the objective lens and the eyepiece.
Thus, 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.
