Question

In optical microscopy, which one of the following combinations of wavelength ($\lambda$) and numerical aperture (NA) provides the best spatial resolution?

• A. $\lambda = 400$ nm and NA = 1.0
• B. $\lambda = 600$ nm and NA = 1.2
• C. $\lambda = 400$ nm and NA = 1.2
• D. $\lambda = 600$ nm and NA = 1.0

Hint:

To achieve the best spatial resolution in optical microscopy, use a short wavelength of light and a high numerical aperture. A smaller wavelength and higher NA result in better resolution.

Answer 1

The Correct Option is C

The spatial resolution \( R \) of an optical microscope is given by the equation: \[ R = \frac{\lambda}{2 \cdot {NA}} \] where \( \lambda \) is the wavelength of light and NA is the numerical aperture. To get the best spatial resolution, we need to minimize \( \lambda \) (the wavelength) and maximize NA (the numerical aperture). 
Step 1: Understanding the options - Option (A): $\lambda = 400$ nm and NA = 1.0 - Here, the resolution is \( R = \frac{400}{2 \cdot 1.0} = 200 \) nm. 
- Option (B): $\lambda = 600$ nm and NA = 1.2 - The resolution is \( R = \frac{600}{2 \cdot 1.2} = 250 \) nm. 
- Option (C): $\lambda = 400$ nm and NA = 1.2 - The resolution is \( R = \frac{400}{2 \cdot 1.2} = 166.67 \) nm. This provides the best spatial resolution. 
- Option (D): $\lambda = 600$ nm and NA = 1.0 - The resolution is \( R = \frac{600}{2 \cdot 1.0} = 300 \) nm. 
Step 2: Conclusion The combination of \( \lambda = 400 \) nm and NA = 1.2 (Option C) provides the best spatial resolution, as it gives the smallest value for \( R \).