Interference of Light Beams

In order to understand the ratio of intensities of bright and dark parts of the resultant pattern, let's first understand the concept of interference of light beams.

When two light beams of the same frequency and coherent with each other meet, they interfere with each other. This interference can be either constructive or destructive, depending on the phase difference between the two beams.

Constructive interference occurs when the phase difference between the two beams is an integer multiple of the wavelength of light. In this case, the amplitudes of the two beams add up, resulting in a brighter pattern.

Destructive interference occurs when the phase difference between the two beams is an odd multiple of half the wavelength of light. In this case, the amplitudes of the two beams cancel each other out, resulting in a darker pattern.

Intensity of Light Beams

The intensity of a light beam is defined as the power per unit area carried by the beam. It is directly proportional to the square of the amplitude of the wave.

Mathematically, intensity (I) is given by the equation: I = A^2, where A is the amplitude of the wave.

Ratio of Intensities

Let's consider two monochromatic light beams with intensities of 16 and 9 units, respectively.

The ratio of intensities can be calculated as follows:

Ratio of Intensities = Intensity of Bright Parts / Intensity of Dark Parts

In constructive interference, the intensity of the bright parts is the sum of the intensities of the individual beams, while the intensity of the dark parts is zero.

So, in this case, the ratio of intensities is:

Ratio of Intensities = (16 + 9) / 0 = 25 / 0

However, dividing by zero is undefined, so this ratio cannot be determined.

In destructive interference, the intensity of the bright parts is zero, while the intensity of the dark parts is the sum of the intensities of the individual beams.

So, in this case, the ratio of intensities is:

Ratio of Intensities = 0 / (16 + 9) = 0 / 25 = 0

Conclusion

From the above calculations, we can see that the ratio of intensities cannot be determined in the case of constructive interference, as it involves dividing by zero. However, in the case of destructive interference, the ratio of intensities is 0.

Therefore, the correct answer is option 'B' (49/1), which represents the ratio of intensities in the case of destructive interference.