Answer :
The size of the shadow cast by the 2-meter obstacle placed 3 meters away from two point light sources located 1.5 meters apart would be approximately 2.25 meters, with an interference pattern characterized by alternating bright and dark regions due to the wave nature of light.
The situation described involves a phenomenon known as the "alternate-inner triangle" principle. When two point light sources are placed at a distance of 1.5 meters apart and a 2-meter obstacle is positioned 3 meters away from the light sources, the size of the shadow and the pattern it produces can be determined using similar triangles.
The shadow size can be calculated by considering the two triangles formed: one connecting the top of the obstacle to each light source and the other connecting the bottom of the obstacle to each light source. These triangles are similar due to the common angle formed by the light sources and the obstacle's top or bottom. Using the property of similar triangles, you can set up a proportion to find the length of the shadow cast by the obstacle.
Let h be the height of the shadow, then:
h / 2 = (3 + 1.5) / 2
h = 2.25 meters.
The pattern produced by this setup would show alternating bright and dark regions, known as interference fringes, due to the wave nature of light and the path-length difference between the two light sources. The bright regions correspond to constructive interference, where the light waves from both sources reinforce each other, while the dark regions correspond to destructive interference, where the waves cancel out.
In summary, the size of the shadow cast by the 2-meter obstacle placed 3 meters away from two point light sources located 1.5 meters apart would be approximately 2.25 meters, and the pattern would exhibit alternating bright and dark regions due to interference effects arising from the wave nature of light.
To learn more about interference pattern refer here:
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