Question

If two coherent light waves produce minima of fifth-order, the path difference between the waves is

• A. $5\lambda$
• B. $\frac{5\lambda }{2}$
• C. $\frac{7\lambda }{2}$
• D. $\frac{9\lambda }{2}$

Answer 1

The correct option is D

$\frac{9\lambda }{2}$

Step 1: Interference

1. An important consequence of the principle of superposition is that when two beams of light intersect, the propagation of each beam is completely unaffected by the presence of the other.
2. However, in the region of crossing both the beams act simultaneously and we expect a change in intensity.
3. A case of utmost importance occurs when monochromatic waves of light from two sources proceed almost in the same direction and superpose at a point either in the same or in the opposite phase.
4. Then the intensity of light at a point that point will be maximum or minimum according to as the waves meet the point in the same or in the opposite phase.
5. This phenomenon is known as interference of light.
6. This phenomenon requires its explanation that light must have a wave nature.
7. 

Step 2: Calculate the Path Difference

Two coherent light waves produce minima of fifth-order

Path difference for destructive order $=\left(2n+1\right)\frac{\lambda }{2}$

where $n=0,1,2\dots ..$

For the 5^th order $n=4$

$\therefore$Path difference $=(2\times 4+1)\frac{\lambda }{2}$

$=\frac{9\lambda }{2}$

Hence, the correct answer is option (D).