A square has sides of length L. In the lower-right and lower-left corners there are two sources of light waves, one in each corner, that emit identical in-phase light waves of wavelength 8.28 m in all directions. What is the minimum value of L such that constructive interference occurs in the upper-right corner? Ignore any reflections.
To find the minimum value of L such that constructive interference occurs in the upper-right corner, we need to consider the path difference between the two sources of light waves.
Constructive interference occurs when the path difference between the two waves is equal to a whole number of wavelengths.
In this case, the path difference can be determined by looking at the triangle formed by the two sources and the upper-right corner of the square.
Let's consider the distance from each light source to the upper-right corner. Since the sources are located in the lower-right and lower-left corners, the distance from each source to the upper-right corner along the sides of the square is L.
Now, consider the distance between the two sources. This can be calculated using the Pythagorean theorem because the distance between the two corners of a square is the square root of twice the square of the side length.
The distance between the two sources is therefore √(2L²).
In order to have constructive interference, the path difference between the two sources should be equal to a whole number of wavelengths. So we can write the following equation:
√(2L²) = n * λ
Where n is the number of wavelengths and λ is the wavelength of the light waves.
To find the minimum value of L, we want to find the smallest n that satisfies this equation. We can rewrite the equation as:
L = (n/√2) * (λ/2)
Since we are interested in the minimum value of L, we want n to be as small as possible, which is n = 1.
Substituting n = 1, we get:
L = (1/√2) * (8.28 m/2)
L ≈ 2.93 m
Therefore, the minimum value of L such that constructive interference occurs in the upper-right corner is approximately 2.93 meters.