Question

A compound microscope having ${f_0} = 7mm,{f_c} = 20mm$ and distance between the lenses is 20cm. If an image is formed at least distance of distant vision, then magnifying power?
(A) 388
(B) 400
(C) 220
(D) 120

Answer 1

Hint: The microscope that uses two sets of lenses is a compound microscope. This will help in obtaining higher magnification. The ratio between the image dimensions and the object is called magnifying power. The compound microscope is very simple and easy to handle. The magnifying power of a compound microscope can be 4x, 10x, or 40x.
Formula used:
To solve this type of question we use the following formula.
$m = - \dfrac{L}{{{f_0}}}\left( {1 + \dfrac{D}{{{f_e}}}} \right)$
Here, m is the magnification and L is the distance between two lenses.

Complete step by step answer:
 Let us first write the information given in the question.
${f_0} = 7mm$,${f_c} = 20mm$, $L = 20cm$, $D = 25cm$
In the case of the image formed at the least distance of distinct vision is given below.
$m = - \dfrac{L}{{{f_0}}}\left( {1 + \dfrac{D}{{{f_e}}}} \right)$
Let us substitute the values in the magnification formula.
$m = - \dfrac{{20}}{{0.7}}\left( {1 + \dfrac{{25}}{2}} \right)$
Let us further simplify the expression.
$m = - \dfrac{{200}}{7}\left( {\dfrac{{27}}{2}} \right)$
$m = - 385.71$

Hence, option (A)”388” is the correct option.

Additional information:
The compound pendulum is an optical device used to see a small object which cannot be seen by the naked eyes.
For the large magnifying power, the focal length of the objective lens and eye lens has to be small. And the focal length of the eye lens is always larger than the focal length of the objective lens to increase the field of view of the microscope

Note:
The least distance of distinct vision of the normal eye is 25cm.
In a compound microscope, the objective is a convex lens of short focal length and aperture, the eyepiece is a convex lens of short focal length but large aperture.
In a compound microscope, the objective and eyepiece are placed at a fixed distance from each other. To focus on an object, the distance of the objective lens is changed from the object.