The letter below represents a $3 \lambda $ difference in path length?


A) Position A
B) Position B
C) Position C
D) Position D
E) Position E

Hint: The path difference in the center is zero. The intensity falls to zero as we move towards right or left and reaches the minimum and then there is the region of minimum. From the centre, the path difference at every maxima becomes $\lambda $.

Complete step by step answer:
The difference between the path traversed by the waves is known as path difference. It is represented by $\Delta x$ whose unit is metre $\left( m \right)$.The formula for calculating the path difference is –
$\Delta x = \dfrac{\lambda }{{2\pi }}\Delta \phi $

where, $\Delta \phi $ is the phase difference.

From the figure above in the question, in the centre the path difference is zero. The path difference can be found by the variation of intensity. When we move towards right or left then the intensity falls to zero and we reach the minimum. So, the region we get is the region of minima. After this we get the region of high intensity and the distance between two peaks have the path difference of length $\lambda $ at every maxima. Hence, at the centre the path difference is zero so, the position E represents the path difference $3\lambda $.

Hence, the correct option is (E).


Note: Two waves, each emitted by the same source, can reach a point by travelling different paths. When this happens, Interference can occur.

The path difference is of two types:
1) Optical path difference
2) Geometrical path difference