A slit of width $a$ is illuminated by light of wavelength $\lambda$. The linear separation between $1^{\text {st }}$ and $3^{\text {rd }}$ minima in the diffraction pattern produced on a screen placed at a distance $D$ from the slit system is $\_\_\_\_$ .

A telescope with objective diameter $R$ is used to observe a distant star emitting light of wavelength 500 nm , at a resolution of $5 \times 10^{-7}$ radian. The value of $R$ is

$\_\_\_\_$ cm .

An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave.

Given below are two statements :

Statement I : A plane wave after passing through prism remains as plane wave but passing through small pin hole may become spherical wave.

Statement II : The curvature of a spherical wave emerging from a slit will increase for increasing slit width.

In the light of the above statements, choose the correct answer from the options given below :