Question

Explain Lorentz-Fitzgerald contraction with an example.

Answer 1

Length Contraction:
Consider two frames of references S and S' to be initially at rest. A rod is placed in the frame of reference S' and an observer O is in S(figure). The length of the rod is $l$ in S' and as measured by the observer in S is $l_o$.
Now the frame of reference S' moves with a velocity $v$ along the positive X-axis. Now, the length of the rod is measured as $l$ by the observer in S. Then $l=l_o\sqrt{1-\frac{v^2}{c^2}}$
i.e., $l<l_o$
Thus the length of the rod moving with a velocity $v$ relative to the observer at rest is contracted by a factor $\sqrt{1-\frac{v^2}{c^2}}$ in the direction of motion. This is known as Lorentz-Fitzgerald contraction.
Example: A circular object will appear as an ellipse for a fast moving observer as shown in figure.