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.

Question

Quizplus · Accepted Answer

The condition for constructive interference is given by:

d sinθ = m λ

where d is the distance between the two sources (which is equal to the length of the side of the square), θ is the angle between the line connecting the sources and the line to the point of interest (in this case, the upper-right corner), m is an integer representing the order of the interference (m=1 for the first maximum), and λ is the wavelength of the light.

For the first maximum, we want to find the smallest value of L that satisfies this equation for m=1 and θ=45° (since the sources are emitting light in all directions, the angle between them and the point of interest is 45° in this case).

Substituting the values given, we get:

L (sin45°) = (1) (8.28 m)

Simplifying, we get:

L = 11.7 m

Therefore, the minimum value of L such that constructive interference occurs in the upper-right corner is 11.7 m, which is closest to choice D (20.0 m).

A Square Has Sides of Length L