Question

Two sources emit microwaves of wavelength = 2.7 cm in phase. How far must they be from each other so that the first and third constructive interference fringes on the same side of the central peak are separated by an angle of 13 degrees?

Answer 1

The distance between the two sources for the first and third constructive interference fringes to be separated by an angle of 13 degrees is approximately 0.104 m.

Step-by-step explanation:

To determine the distance between the two sources for the first and third constructive interference fringes to be separated by an angle of 13 degrees, we can use the equation for constructive interference:

d*sin(theta) = m * lambda

In this equation, d is the distance between the sources, theta is the angle between the fringes, m is the order of the interference fringe, and lambda is the wavelength of the microwaves.

By substituting the given values, we have:

2*d*sin(13 degrees) = 2 * lambda

The distance between the sources, d, can be calculated by rearranging the equation:

d = lambda / (2*sin(13 degrees))

Substituting the given wavelength of 2.7 cm (or 0.027 m), we can find the distance between the sources:

d = 0.027 m / (2*sin(13 degrees))