Question

In the Roman soldier model for refraction, a muddy stream crosses the road they are on walking on at 45°. Will the soldiers in the front row all hit the water at the same time?

A. Sometimes
B. Yes
C. No
D. Not enough info

Answer 1

C. No.

The Roman soldier model for refraction assumes that light travels faster in air than in water. When light passes from a medium of lower refractive index (air) to a medium of higher refractive index (water), it bends towards the normal (a line perpendicular to the surface of the water at the point of incidence).

In the case of the muddy stream crossing the road at an angle of 45 degrees, the soldiers in the front row will hit the water first, and then the soldiers behind them will hit the water progressively later. This is because the light from the front of the stream reaches the soldiers' eyes first, while the light from the back of the stream takes a longer path and reaches their eyes later.

Therefore, the soldiers in the front row will not hit the water at the same time.

Answer 2

In the Roman soldier model for refraction, it is assumed that the soldiers in the front row will walk at a constant speed and in a straight line. However, if the stream they are crossing is muddy, it is likely that the water will slow down some of the soldiers more than others due to differences in depth and the resistance of the mud.

Therefore, even if the soldiers in the front row are lined up perfectly and walk at the same speed, they may not all hit the water at the same time due to the uneven terrain and the resistance of the mud. Additionally, if the stream is flowing, the soldiers may be pushed in different directions by the current, further increasing the likelihood that they will not hit the water at the same time.

Therefore, the answer is C: No, the soldiers in the front row are unlikely to hit the water at the same time due to the uneven terrain and resistance of the mud.