As sunlight enters the Earth\'s atmosphere, it changes direction due to the smal

Question

As sunlight enters the Earth's atmosphere, it changes direction due to the small difference between the speeds of light in vacuum and in air. The duration of an optical day is defined as the time interval between the instance when the tip of the rising Sun is just visible above the horizon and the instant when the tip of the sun just disappears below the horizontal plane. The duration of the geometric day is defined as the time intercal between the instant a mathematically straight line between an observer and the top of the Sun just clears the horizon and the instant this line just dips below the horizon.

(a) Explain wich is longer, an optical day or a geometric day.

(b) Find the difference between these two time intervals. Model the Earth's atmosphere as uniform, with index of refraction 1.000293, a sharply defined upper surface, and depth 8614m. Assume the observer is at the Earth's equator so that apparent path of the rising and setting Sun is perpendicular to the horizon.

Explanation / Answer

due tio refraction, rays will bend below the geonetrical st line and increases optical length

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snells law na sinA = nb sin B

sin B = 1/1.000293

B= 88 deg

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angle of Horizon -= 90 -88.61 = 1.36

totAL INCREASE OF ANGLE = 2* 1.36 = 2.77 DEG

FRO 180 DEG = 12 HRS

SO FOR

182.77 DEG . TOITAL TIME = 12.184 HRS

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