The figure displays a glowing mercury tube. The intensities at...

The glowing mercury tube acts as a finite line source of light.

The intensity of light at a given point depends on its distance from the source elements and the angle at which the light rays arrive. The illuminance is given by $E = \int \dfrac{dI}{r^2} \cos \theta$.

Point A is located on the perpendicular bisector of the tube. For this point, the average distance $r$ to the various elements of the tube is minimum, and the light rays strike most directly ($\cos \theta$ is maximum). Hence, the intensity is maximum at A.

Points B and C are symmetrically placed on either side of A, further away from the center of the tube. For these points, the average distance to the tube's elements is greater, and the light rays arrive more obliquely ($\cos \theta$ is smaller).

Therefore, the intensity decreases as we move from A towards B or C.

Due to the symmetrical placement of B and C with respect to the center of the tube, the intensity at B is equal to the intensity at C.

Thus, the intensities are related as $I_A > I_B = I_C$, which can be written as $B = C < A$.