State the condition under which no change in the direction of propagation of light ray will take place when it passes from medium a to medium b
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Answer:
The wave property of light (an observed classification of its propagation properties) causes a ray of light to refract (bend) when as it passes into or out of materials with different supported light speed.
You asked why a ray of light does not bend when passing into a material perpendicular to the boundary. This is rather easy to explain. No math is required. To understand, I shall first explain why it bends when it makes contact at any other angle…
Think of a ray of light as two wheels connected by an axle. The wheels are zipping north on a straight road at 100 kilometers per hour. The road has just enough downhill grade to maintain the speed with a force that balances the road friction and wind.
But suddenly the wheels hit a dirt road that crosses the pavement at an angle (see diagram below). The angled road is soft dirt, and the force that propels the wheels can only manage a steady speed of 75 kph on that road.
But, note that the right wheel hits the angled road first, and so it slows before the left wheel—as shown in the upper image of the wheels. As the right wheel slows, the left wheel continues for a fraction of a second at the faster speed and this begins to turn the axle to the right.
This wheel analogy is actually more than an analogy. It is exactly what happens when waves refract. In fact, the calculation for the angle of refraction can be extrapolated from this drawing and the difference in speeds—for all refraction (even for concave and convex lenses).
But, when the wheels hit a perpendicular road—even if their speed is suddenly reduced—they do not turn, because the two wheels are reduced at the exact same time. They continue straight, but at reduced speed. There is no extra high-speed travel time on one wheel compared to the other.
Incidentally, in the diagram above, let’s assume that the entire area north of the dirt road is paved for high-speed travel (even to the left and right of the grey road). In this case, then the wheels will emerge parallel to their original direction of travel, but they will be traveling off road. They will emerge to the right of the grey road shown in the figure.