Question

A simple microscope consists of a concave lens of power $10D$ and a convex lens of power $15D$ . Its magnification at near point is
(least distance of distinct vision, $D = 25cm$ )

Answer 1

Hint: In order to this question, to calculate the magnification, we will find the focal length of the concave lens of the microscope and then the focal length of the convex lens. And then we will find the actual focal length of the simple microscope, now we can find its magnification.

Complete step-by-step solution:
The power of both the lenses is given, then we will find the focal lengths of both the lenses first.
So, the power of a concave lens is $10D$ .
Focal length of the concave lens, $f = - \dfrac{{100}}{{10}} = - 10cm$
And, the power of a convex lens is $15D$ .
Focal length of the convex lens $ = \dfrac{{100}}{{15}} = 6.67cm$ .
Now, using
$
  \dfrac{1}{f} = \dfrac{1}{{{f_1}}} + \dfrac{1}{{{f_2}}} \\
   \Rightarrow \dfrac{1}{f} = \dfrac{1}{{10}} + \dfrac{1}{{6.67}} \\
   \Rightarrow f = \dfrac{{6.67 \times 10}}{{10 - 6.67}} = 20cm \\
 $
Now, we can find the magnification at the near point, as we have focal lengths of both the lenses.
$
  \therefore m = 1 + \dfrac{D}{F} \\
  \,\,\,\,\,\,\,\, = 1 + \dfrac{{25}}{{20}} = 2.25 \\
 $
So, the magnification of the microscope is $2.25$ .

Note: The field of view refers to the amount of your specimen or object that can be seen through the microscope. You can see 5mm at a magnification of $40x$ . You can see $2mm$ at a magnification of $100x$ . At $400x$ magnification, \[0.45mm,{\text{ }}or{\text{ }}450{\text{ }}microns\] , can be seen. At $1000x$ magnification, \[0.180mm,{\text{ }}or{\text{ }}180{\text{ }}microns\] , can be seen.