Question
Give the reason for the advanced sunrise and delayed sunset.
✓
Answer
- As the altitude (height) from the earth’s surface gradually increases, the earth’s atmosphere becomes rarer.
- Hence, the refractive index of the air decreases continuously.
- So a ray of light coming from the Sun towards an observer continuously passes from an optically rarer to optically denser medium and bends towards the normal.
- Thus, its direction of propagation changes continuously.
[Actual and apparent position of the Sun at sunrise / sunset]
- The actual sunrise or sunset begins when the Sun reaches the horizon.
- In figure, $S_1$ is the actual position of the Sun a little below the horizon.
- In this case, the light rays coming from $S _1$, continuously get refracted in the earth's atmosphere (atmospheric refraction) and reach the observer as shown in the figure.
- The tangent drawn to the curved path of the ray at point $P$ passes through $S_2$, above the horizon.
- $S_2$ is the apparent position of the Sun.
- Thus, during the sunrise, the Sun is seen even though it is little below the horizon.
- Similarly, during the sunset it is seen for sometime even though it is little below the horizon.
- Taking the refractive index of air as $1.00029$ the apparent angular shift in the position of the Sun is found to be approximately $\left(\frac{1}{2}\right)^{\circ}$
- Now, for angular displacement of $180^{\circ}$ of the Sun, time required is $12$ hours. Hence for angular displacement of $\left(\frac{1}{2}\right)^{\circ}$ of the Sun, time required is
- $=\frac{\left(\frac{1}{2}\right) \times 12 \text { hours }}{180^{\circ}}$
- $=0.03333$ hour
- $=1.9998$ minutes
- $=2$ minutes
- Due to advance sunrise and delayed sunset the duration of a day increases by about $4$ minutes.
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