When viewed from the window of a moving train

Explain this common observation clearly: If you look out of the window of a fast moving train, the nearby trees, houses etc. seem to move rapidly in a direction opposite to the train’s motion, but the distant objects hill tops, the Moon, the stars etc. seem to be stationary. In fact, since you are aware that you are moving, these distant objects seem to move with you.

Solution

Line of sight is defined as an imaginary line joining an object and an observer’s eye. When we observe nearby stationary objects such as trees, houses, etc. while sitting in a moving train, they appear to move rapidly in the opposite direction because the line-of-sight changes very rapidly. (adsbygoogle = window.adsbygoogle || []).push({}); On the other hand, distant objects such as trees, stars, etc. appear stationary because of the large distance. As a result, the line of sight does not change its direction rapidly.

When looking through the window of a moving train, the nearby trees/objects appear to move in the opposite direction. The faraway trees appears to be stationary. This can be explained by the concept of relative velocity and perception of motion by the eye.

Let the train moves with a velocity $\vec{v}_A$ (relative to the ground). The velocity of the tree is $\vec{v}_B=\vec{0}$. The velocity of the tree relative to the train is $\vec{v}_{B/A}=\vec{v}_B-\vec{v}_A=-\vec{v}_A$. Thus, for a person sitting in the moving train, nearby trees appear to move in opposite direction.

The eye perceives velocity as the angular velocity of the line of sight (the line from eye to the object). The angular velocity of faraway objects is very small which makes faraway trees appear as stationary. It is similar to the illusion as if the moon is following us.

Assertion Reasoning Problem From IIT JEE 2008

Problem:

Statement 1: For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.

Statement 2: If the observer and the object are moving at velocities $\vec{v}_1$ and $\vec{v}_2$ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $\vec{v}_2-\vec{v}_1$.

1. Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1.
2. Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1.
3. Statement 1 is true, statement 2 is false.
4. Statement 1 is false, statement 2 is true.

Solution:

Both, statement 1 and statement 2 are true but statement 2 is not a correct explanation of statement 1. The relative velocity of the nearby, as well as the far-off objects, is the same.

The explanation has to do with how human mind/eye perceive the motion. Take a simple situation of two point objects $\mathrm{O_1}$ and $\mathrm{O_2}$ (see figure). The images $\mathrm{I_1}$ and $\mathrm{I_2}$ formed on the retina of eye are point images. As the object moves, the image on the retina also moves. The distance moved by the image on the retina is perceived as motion/velocity. Since eye is a lens with distance of retina/screen w.r.t. lens almost fixed, the angular displacement of the image in a given time is perceived as velocity. For same relative velocity of objects $\mathrm{O_1}$ and $\mathrm{O_2}$, angular displacement of nearby object ($\theta_1$ in the figure) is more than the angular displacement of the far-off object ($\theta_2$). Hence nearby objects appear to move faster.

References and External Links

1. IIT JEE Physics by Jitender Singh and Shraddhesh Chaturvedi
2. Why does one get an illusion as moon following him? (physics.stackexchange.com)

Explain this common observation clearly : If you look out of the window of a fast moving train, the nearby trees, houses etc. seem to move rapidly in a direction opposite to the train’s motion, but the distant objects (hill tops, the Moon, the stars etc.) seem to be stationary. (In fact, since you are aware that you are moving, these distant objects seem to move with you)

Line of sight is defined as an imaginary line joining an object and an observer’s eye. When we observe nearby stationary objects such as trees, houses, etc. while sitting in a moving train, they appear to move rapidly in the opposite direction because the line of sight changes very rapidly.

On the other hand, distant objects such as trees, stars, etc. appear stationary because of the large distance. As a result, the line of sight does not change its direction rapidly.

The line joining a given object to our eye is known as the line of sight. When a train moves rapidly, the line of sight of a passenger sitting in the train for nearby trees changes its direction rapidly. As a result, the nearby trees and other objects appear to run in a direction opposite to the train’s motion. However, the line of sight of distant and large size objects e.g., hill tops, the Moon, the stars etc., almost remains unchanged (or changes by an extremely small angle). As a result, the distant object seems to be stationary.

Concept: Measurement of Length

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