1. Resultant intensity formula

For two coherent sources of equal intensity $I_0$, the resultant intensity at a point is

Since the two sources are equally intense,

so

where $\Delta\phi$ is the total phase difference at the observation point.

2. Given source phase difference

Source $P$ is ahead of source $Q$ by $90^\circ$. Thus initial phase difference is

Also, wavelength is

and separation between sources is

3. Path difference at points $A$, $B$, $C$

From the figure (standard geometry here), the three points are equidistant from the midpoint of $PQ$ and lie along directions such that the path differences are:

• At $A$: $\Delta r = +5\,\text{m}$
• At $B$: $\Delta r = 0$
• At $C$: $\Delta r = -5\,\text{m}$

So the corresponding phase differences due to path are

Since

for $\Delta r = 5$ m,

Thus,

• At $A$: path phase difference $= +\frac{\pi}{2}$
• At $B$: path phase difference $= 0$
• At $C$: path phase difference $= -\frac{\pi}{2}$

4. Total phase difference at each point

Taking total phase difference as

we get:

At $A$

Hence,

At $B$

Hence,

At $C$

Hence,

5. Intensity ratio

Therefore,

6. Compare with options

This matches:

So the correct option is C.

7. Comparison with stored answer

Stored correct answer is B: $2:1:0$, but the derived answer is C: $0:1:2$.

Hence, I disagree with the stored answer. The likely reason is that points $A$ and $C$ were interchanged while interpreting the geometry. If the labels are in the opposite order, the ratio becomes $2:1:0$, but for the natural left-to-right ordering with path differences $+5,0,-5$, the ratio is $0:1:2$.