Page 219 - Physics_Form_2

Optical instruments

Magnification of a simple microscope angular magnification, M, and is given
A simple microscope magnifies an θ image
object by increasing its angular size. The by, M = θ
magnification produced by the simple object
microscope depends on the focal length of The angular magnification should not
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the lens. Lenses of short focal length give be confused with the linear or lateral
larger magnification than those with long magnification, m, of a simple lens, which
focal length. In Figure 6.2(a), the object is the ratio of the image height, hi, to the
is at the near point, where it subtends an h
angle θ object to the eye. On the other hand, object height, ho, given by, m = h i
in Figure 6.2(b), the magnifier in front o
of the eye forms an image far away from Linear magnification is also given by the
ratio of the image distance, v, to the object
the lens; the image subtends an angle v
θ image at the magnifier. The usefulness distance, u. That is: m = u
of the magnifier is given by the ratio v h
of the angle subtended by the image It follows that, u = h i and thus,
(θ ) to the angle subtended by the h o
image vu i .
object ( θ ). This ratio is called the h
object o

To find the value of angular magnification, let the angles subtended by the object and the

image be very small, such that, sinθ = tanθ ≈ θ and sinθ = tanθ ≈ θ .
object object object image image image
,
Suppose the object in Figure 6.2 has a height, h and it is placed at the focal point, f
o
= D = 25 cm, where it subtends an angle θ object . If the angleθ object is very small, then,

h
tanθ ≈ θ = o .
object object D

The virtual image formed by the lens subtends a small angle θ image such that,
h uh
tanθ ≈ θ = i . But v = i
image image v h o
h h
Therefore, tanθ image ≈ θ image = h × o = o .
i
uh
i u
θ h h h D D
Now, M = image = o ÷ o = o × =
θ object u D u h o u

D
Hence, angular magnification, M = .
u
1 1 1
Using the lens formula, = +
f u v

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Physics Form 2 Final.indd 213 25/10/2025 10:28