Question

Under what condition will the magnifying power of a microscope be maximum?

Hint:

Remember this trade-off for microscopes and telescopes: \textbf{Maximum Magnification} \(\implies\) Final image at Near Point (D) \(\implies\) \textbf{Maximum Eye Strain}. \textbf{Normal Adjustment} \(\implies\) Final image at Infinity \(\implies\) \textbf{Relaxed Eye}.

Answer 1

Step 1: Understanding the Concept:
The magnifying power (or angular magnification) of a microscope is a measure of how much larger the image appears compared to the object when viewed through the instrument. This power depends on the focal lengths of the lenses and the position of the final image.
Step 2: Key Formula or Approach:
The magnifying power (\(M\)) of a compound microscope is the product of the magnification of the objective lens (\(m_o\)) and the eyepiece (\(m_e\)):
\[ M = m_o \times m_e \] The magnification of the eyepiece is given by:
\[ m_e = \left(1 + \frac{D}{f_e}\right) \quad \text{(for final image at near point D)} \] \[ m_e = \frac{D}{f_e} \quad \text{(for final image at infinity)} \] where \(D\) is the least distance of distinct vision and \(f_e\) is the focal length of the eyepiece.
Step 3: Detailed Explanation:
From the formulas above, it is clear that the value of \(m_e\) is greater when the final image is formed at the near point \(D\) compared to when it is formed at infinity.
\[ \left(1 + \frac{D}{f_e}\right)>\frac{D}{f_e} \] Since the overall magnifying power \(M\) is directly proportional to \(m_e\), the microscope achieves its maximum magnifying power when the eyepiece is adjusted to form the final virtual image at the least distance of distinct vision, \(D\).
This condition, however, causes the most strain on the observer's eye, as the eye muscles are fully tensed to focus at the near point. The alternative setting, where the final image is at infinity, is called "normal adjustment" because it allows for more relaxed viewing.
Step 4: Final Answer:
The condition for maximum magnifying power is that the eyepiece must be positioned such that the final virtual image is formed at the near point (\(D\)) of the eye.