Abbe's Equation and Microscopy Resolution
Abbe's equation defines the theoretical limit of resolution in light microscopy. The smallest distance ($d$) at which two points can be distinguished is given by the formula:
$d = \frac{\lambda}{2 \times NA}$
Where:
- $d$ is the minimum resolvable distance.
- $\lambda$ is the wavelength of the light used.
- $NA$ is the numerical aperture of the objective lens.
Factors Affecting Resolution
Based on Abbe's equation, the resolution ($d$) is directly proportional to the wavelength ($\lambda$) and inversely proportional to the numerical aperture ($NA$). Therefore, to resolve smaller details (i.e., achieve a smaller $d$), one needs shorter wavelengths and higher numerical apertures.
Evaluating the Options
- Wavelength ($\lambda$): A key component of the equation. Shorter wavelengths improve resolution.
- Numerical aperture ($NA$): Another key component. Higher NA improves resolution.
- Magnification: While important for viewing details, magnification itself does not determine the resolution limit. It only enlarges the image.
- Intensity of incident light: Affects image brightness and contrast but not the fundamental limit of separability imposed by diffraction.
Thus, the ability to resolve two entities depends on the wavelength and the numerical aperture of the objective lens.
The correct factors are Wavelength (C) and Numerical aperture of the objective lens (D).
Important Questions from Numerical Computation
In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core branches is 1/4th of the number of students who like other branches. The number of students who like both their core and other branches is 500.
The number of students who like their core branches is$A$ is an ($n \times n$) matrix. Consider the following two statements
Statement 1: Columns of matrix $A$ are linearly independent
Statement 2: Inverse of matrix $A$ exists
Which one of the following statements is TRUE?
- Consider the function $G(x, y, z) = 0$. This function allows us to implicitly define each of three variables as a function of the other two variables. Assume that all partial derivatives of the function $G(x, y, z)$ exist everywhere. Then, the value of $\left(\frac{\partial z}{\partial x} \times \frac{\partial x}{\partial y} \times \frac{\partial y}{\partial z}\right)$ is _________ (in integer)
- Levenshtein distance is used to measure the minimum edit distance between two strings by counting the minimum number of editing operations (such as, insertions, deletions, substitutions) required to transform one string to another. Consider an alternative version of the Levenshtein distance in which each insertion and each deletion has a cost of 1 and substitutions are not allowed.
Based on this alternative version, the Levenshtein distance between the strings, word and work is ______ (Answer in integer). - In a given collection of documents, let $N$ be the total number of documents and let $d$ be the number of documents in which the term $t$ occurs.
Which ONE of the following fractions is used to define the inverse document frequency (idf) of the term $t$?
