Question

The length of the tube of a compound microscope is 15 cm. The focal length of objective and eye lenses are 1 cm and 5 cm respectively. What is the magnifying power of the microscope for the relaxed vision?
${\text{A}}{\text{.}}$ 50
${\text{B}}{\text{.}}$ 75
${\text{C}}{\text{.}}$ 25
${\text{D}}{\text{.}}$ 100

Answer 1

Hint: Here, we will proceed by using the formula for the calculation of the magnifying power of a compound microscope for relaxed vision in terms of length of the tube, focal lengths of the objective lens and eye lens.
Formula Used: ${\text{m}} = \dfrac{{{\text{L}} \times {\text{D}}}}{{{{\text{f}}_{\text{o}}} \times {{\text{f}}_{\text{e}}}}}$.

Complete Step-by-Step solution:
Given, Length of tube of compound microscope, L = 15 cm
Focal length of the objective lens, ${{\text{f}}_{\text{o}}}$ = 1 cm
Focal length of the eye lens, ${{\text{f}}_{\text{e}}}$ = 5 cm
As we know that the formula for the magnifying power of a compound microscope for relaxed vision is given by
Magnifying power of the microscope for relaxed vision, ${\text{m}} = \dfrac{{{\text{L}} \times {\text{D}}}}{{{{\text{f}}_{\text{o}}} \times {{\text{f}}_{\text{e}}}}}{\text{ }} \to {\text{(1)}}$ where L denotes the length of the tube of the compound microscope, ${{\text{f}}_{\text{o}}}$ denotes the focal length of the objective lens, ${{\text{f}}_{\text{e}}}$ denotes the focal length of the eye lens and D denotes the least distance for distinct vision which is equal to 25 cm for a normal eye (D = 25 cm)
By substituting L = 15 cm, ${{\text{f}}_{\text{o}}}$ = 1 cm, ${{\text{f}}_{\text{e}}}$ = 5 cm and D = 25 cm in the formula given by equation (1), we get
$ \Rightarrow {\text{m}} = \dfrac{{{\text{15}} \times {\text{25}}}}{{{\text{1}} \times {\text{5}}}} = 15 \times {\text{5}} = 75$
Therefore, the required magnifying power of the given compound microscope for the relaxed vision is 75.
Hence, option B is correct.

Note- A compound microscope is a microscope with high power (high magnification) which uses a compound lens system. To achieve a high magnification, a compound microscope has multiple lenses through which the objective lens is compounded by the eyepiece lens. Higher magnification is accomplished using two lenses instead of just one single magnifying lens.