The resolving power (\(P\)) of a microscope is given by: \[ P = \frac{2 \mu \sin \theta}{1.22 \lambda}, \] where: \(\mu\) is the refractive index of the medium, \item \(\lambda\) is the wavelength of light.
To improve resolving power: Increasing \(\mu\) (refractive index) improves \(P\), Decreasing \(\lambda\) also increases \(P\).
Let \( a \in \mathbb{R} \) and \( A \) be a matrix of order \( 3 \times 3 \) such that \( \det(A) = -4 \) and \[ A + I = \begin{bmatrix} 1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2 \end{bmatrix} \] where \( I \) is the identity matrix of order \( 3 \times 3 \).
If \( \det\left( (a + 1) \cdot \text{adj}\left( (a - 1) A \right) \right) \) is \( 2^m 3^n \), \( m, n \in \{ 0, 1, 2, \dots, 20 \} \), then \( m + n \) is equal to:
Rate law for a reaction between $A$ and $B$ is given by $\mathrm{R}=\mathrm{k}[\mathrm{A}]^{\mathrm{n}}[\mathrm{B}]^{\mathrm{m}}$. If concentration of A is doubled and concentration of B is halved from their initial value, the ratio of new rate of reaction to the initial rate of reaction $\left(\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}}\right)$ is
A device that processes light waves (or photons), either to enhance an image for viewing or to analyze and determine its characteristic properties is called an optical instrument (or "optic" for short).