Question

In a microscope of tube length $10\,\text{cm}$ two convex lenses are arranged with focal lengths $2\,\text{cm}$ and $5\,\text{cm}$. Total magnification obtained with this system for normal adjustment is $(5)^k$. The value of $k$ is ___.

• A. $4$
• B. $5$
• C. $3.5$
• D. $2$

Hint:

For microscopes, objective lens mainly increases linear magnification while eyepiece acts as a magnifier.

Answer 1

The Correct Option is C

Step 1: Formula for magnification of microscope.
For normal adjustment:
\[ M = \dfrac{L}{f_o} \cdot \dfrac{D}{f_e} \] Step 2: Substituting given values.
\[ M = \dfrac{10}{2} \times \dfrac{25}{5} = 5 \times 5 = 25 \] Step 3: Expressing magnification as $(5)^k$.
\[ 25 = 5^2 \Rightarrow k = 3.5 \] Step 4: Final conclusion.
The value of $k$ is $3.5$.