Intensity of Secondary Maxima in Multi-Slit Interference Pattern

Understanding the Intensity of Secondary Maxima in Multi-Slit Interference Patterns

When eight slits equally separated by 0.149 mm are uniformly illuminated by a monochromatic light at λ=523nm, a specific pattern of interference is observed. One common question that arises in such scenarios is about the intensity of secondary maxima compared to the principal maxima. Let's delve into the details:

The Question:

What is the intensity of a secondary maxima compared to that of the principal maxima?

a. 1/16

b. 1/8

c. 1/4

d. 1/32

Final Answer:

In a multi-slit interference pattern with eight slits illuminated by monochromatic light, the intensity of the first secondary maxima compared to the principal maxima is 1/8. This highlights how the principal maxima are significantly brighter than the secondary maxima. Therefore, the correct answer is b. 1/8.

Explanation:

The question concerns the intensity of secondary maxima compared to the intensity of principal maxima in a multi-slit interference scenario, specifically with eight slits and monochromatic light.

The intensity of secondary maxima in a multiple-slit interference pattern can be determined using the interference function sin^2(Nβ/2) / N^2sin^2(β/2), where N is the number of slits, and β is the phase difference between waves from adjacent slits.

In this case for the eight-slit system, the intensity ratio of the first secondary maxima to principal maxima turns out to be 1/8.

This intensity ratio signifies that the principal maxima are much more intense compared to the secondary maxima, as is typical in multiple-slit interference patterns.