Waves from coherent sources, S1 and S2, produce an interference pattern - Scottish Highers Physics - Question 16 - 2023

To find the wavelength of the waves, we can use the formula for the path difference in terms of wavelength:

$ext{Path Difference} = n imes ext{Wavelength}$

Where:

• n is the order of the maximum (1 for the first maximum, 2 for the second, etc.).
• The path difference here is given as 154 mm.

Assuming we are looking for the first-order maximum (n = 1):

1. Set the equation: $154 ext{ mm} = 1 imes ext{Wavelength}$

2. Thus, the wavelength is: $ext{Wavelength} = 154 ext{ mm}$

However, since this does not match any of the options provided, we should consider multiple maxima. For example, if we consider the second maximum (n = 2), we would divide the path difference by 2, leading to:

ext{Wavelength} = rac{154 ext{ mm}}{2} = 77.0 ext{ mm}

Continuing this logic suggests looking for a lower order maximum. Since the maximums are established at different locations, we need options that give us a valid wavelength likely representing multiple orders of maximum. Therefore, we test each option:

• A. 14.0 mm -> 11 maximums (not fitting)
• B. 15.4 mm -> 10 maximums
• C. 25.7 mm -> 6 maximums
• D. 28.0 mm -> 5 maximums
• E. 30.8 mm -> 4 maximums

Identifying the number of maxima leads to adjusting our approach towards considering the total distance relation based from source alignment. Using E:
With E = 30.8 mm, leading to:

ightarrow n ext{ (approx 5)}$$ Choosing option E, therefore, is justified as the highest fitting order, thus yielding **30.8 mm**.