Question

To improve the resolving power of a compound microscope we should

• A. decrease the diameter of the objective lens.
• B. decrease the focal length of the eye-piece.
• C. increase the refractive index of the medium between the object and objective lens.
• D. increase the wavelength of light.

Hint:

Resolving power of a microscope is 2 mu sin(theta) over 1.22 lambda.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The resolving power of a microscope is
\[ R=\frac{2\mu\sin\theta}{1.22\lambda} \]
where \(\mu\) is the refractive index of the medium between the object and the objective and \(\theta\) is the half-angle of the cone of light.

Step 2: Check the options
(A) Decreasing the objective diameter lowers \(\sin\theta\) and so lowers \(R\).
(B) The eyepiece focal length affects magnification only, not resolving power.
(C) Increasing \(\mu\), for example by using oil, increases \(R\). This is the correct way.
(D) A longer wavelength makes \(R\) smaller. Violet light is better than red.

Step 3: Conclusion
Option (C).

Final Answer:
The resolving power is proportional to the refractive index of the medium at the objective, option (C). \[ \boxed{\text{Increase the refractive index of the medium}} \]