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:

To improve resolution in optical microscopy, use shorter wavelengths of light and objective lenses with higher numerical apertures (NA). However, keep in mind that a higher NA also reduces the depth of field.

Answer 1

The Correct Option is A, C, D

For optical microscopes, the resolution limit and depth of field are related to the wavelength of light, refractive index, and numerical aperture of the objective lens. Let's break down the options:
1. Option (A): Resolution limit decreases with decreasing wavelength of light.
This is correct. The resolution limit \( d \) of an optical microscope is inversely proportional to the wavelength of light used. The shorter the wavelength, the better the resolution. This is described by the Rayleigh criterion, which states that the smallest resolvable distance is approximately \( d = \frac{\lambda}{2 {NA}} \), where \( \lambda \) is the wavelength and NA is the numerical aperture.
2. Option (B): Resolution limit decreases with decreasing refractive index of the medium.
This is incorrect. The resolution limit actually improves (decreases) with increasing refractive index of the medium. The refractive index \( n \) of the medium between the lens and the specimen affects the numerical aperture (NA), and a higher NA improves resolution.
3. Option (C): Depth of field decreases with increasing value of numerical aperture of the objective lens.
This is correct. The depth of field (\( D_f \)) is inversely proportional to the numerical aperture (NA). As the numerical aperture increases, the resolution improves, but the depth of field decreases. This means that with a high NA, only a thin plane of focus is visible at any given time.
4. Option (D): Resolution limit decreases with increasing value of numerical aperture of the objective lens.
This is correct. As the numerical aperture increases, the resolution improves. The numerical aperture is a measure of the lens's ability to gather light and resolve fine detail. Higher NA allows for finer details to be resolved, reducing the resolution limit.
Thus, the correct answers are options (A), (C), and (D).