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: $\text{m}={\displaystyle \frac{\text{L}\times \text{D}}{{\text{f}}_{\text{o}}\times {\text{f}}_{\text{e}}}}$.

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, $\text{m}={\displaystyle \frac{\text{L}\times \text{D}}{{\text{f}}_{\text{o}}\times {\text{f}}_{\text{e}}}}\to \text{(1)}$ 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
$\Rightarrow \text{m}={\displaystyle \frac{\text{15}\times \text{25}}{\text{1}\times \text{5}}}=15\times \text{5}=75$
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.