Question

For a conventional optical microscope, which of the following options regarding the resolution limit and the depth of field is/are correct?

• A. Resolution limit decreases with decreasing wavelength of light
• B. Resolution limit decreases with decreasing refractive index of the medium
• C. Depth of field decreases with increasing value of numerical aperture of the objective lens
• D. Resolution limit decreases with increasing value of numerical aperture of the objective lens

Hint:

Remember: Resolution improves with shorter wavelengths and higher numerical aperture, while depth of field decreases with increasing NA.

Answer 1

The Correct Option is A, C, D

Step 1: Recall resolution formula.
The resolution limit of a microscope is approximately: \[ d \approx \frac{0.61 \lambda}{n \sin\theta} = \frac{0.61 \lambda}{NA} \] where: - \(\lambda\) = wavelength of light, - \(n\) = refractive index of medium, - \(\theta\) = half-angle of light cone, - \(NA = n \sin \theta\) = numerical aperture.

Step 2: Effect of wavelength.
If \(\lambda\) decreases, the denominator is unchanged but numerator decreases, so: \[ d \downarrow \Rightarrow \text{Resolution improves.} \] Thus, statement (A) is correct.

Step 3: Effect of refractive index.
If refractive index \(n\) decreases, \(NA = n \sin \theta\) decreases, hence denominator decreases. This makes \(d\) increase, i.e. resolution worsens. So, resolution limit actually increases with decreasing refractive index. Thus, (B) is incorrect.

Step 4: Effect of numerical aperture on depth of field.
Depth of field (DOF) is approximately: \[ DOF \propto \frac{1}{NA^2} \] So if numerical aperture increases, DOF decreases. Thus, (C) is correct.



Step 5: Effect of numerical aperture on resolution.
From formula: \(d \propto \frac{1}{NA}\). If numerical aperture increases, resolution limit decreases (better resolution). Thus, (D) is correct. Final Answer:
\[ \boxed{(A), (C), (D)} \]