Question

Which of the following statement(s) is/are true for an optical microscope?

• A. Increasing the aperture of the objective lens deteriorates the resolution
• B. Reducing the wavelength of illuminating light improves the resolution
• C. Increasing the refractive index of the medium in between the sample and the objective lens improves the resolution
• D. Reducing the wavelength of illuminating light decreases the depth of field

Hint:

- To improve resolution: use shorter wavelength, higher refractive index medium, and larger aperture.
- But remember: higher resolution often reduces depth of field.

Answer 1

The Correct Option is B, C, D

Step 1: Recall the formula for resolution.
The resolution of an optical microscope is given by Abbe’s equation: \[ d = \frac{0.61 \lambda}{n \sin \theta} \] where - $d$ = minimum resolvable distance, - $\lambda$ = wavelength of light, - $n$ = refractive index of the medium, - $\theta$ = half-angle of the aperture of the objective lens.
Step 2: Analyze statement (A).
- Increasing the aperture ($\sin \theta$ increases) improves resolution (i.e., reduces $d$). - Hence, the statement “it deteriorates the resolution” is false.
Step 3: Analyze statement (B).
- Resolution $d \propto \lambda$. - Reducing $\lambda$ (shorter wavelength light) leads to smaller $d$ $\Rightarrow$ better resolution. - Hence, (B) is true.
Step 4: Analyze statement (C).
- Increasing $n$ (refractive index) increases numerical aperture $NA = n \sin \theta$. - Larger $NA$ $\Rightarrow$ smaller $d$ $\Rightarrow$ improved resolution. - Hence, (C) is true.

Step 5: Analyze statement (D).
- Depth of field is inversely related to resolution. - Using shorter wavelength light improves resolution but reduces depth of field. - Hence, (D) is true. Final Answer: \[ \boxed{\text{(B), (C), and (D)}} \]