Whether an optical day or geometrical day is longer.

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 instant when the top of the rising Sun is just visible above the horizon andthe instant when the top of the Sun just disappears below the horizontal plane. The duration of the geometric day is defined as the time interval between the instant a mathematically straight line between an observer and the top of the Sun just clears the horizon and the instant this linejust dips below the horizon. (a) Explain which 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 1.000 293, a sharply defined upper surface, and depth 8 614 m. Assume the observer is at the Earth’s equator so that the apparent path of the rising and setting Sun is perpendicular to the horizon.

Answer 1

Question

Chapter 25, Problem 62P

(a)

To determine

Whether an optical day or geometrical day is longer.

(b)

To determine

The difference between in the time interval of the optical day and geometrical day.

Expert Solution & Answer

Trending nowThis is a popular solution!

See solution

Check out sample textbook solution

Students have asked these similar questions

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 instant when the top of the rising Sun is just visible above the horizon andthe instant when the top of the Sun just disappears below the horizontal plane. The duration of the geometric day is defined as the time interval between the instant a mathematically straight line between an observer and the top of the Sun just clears the horizon and the instant this linejust dips below the horizon. (a) Explain which 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 1.000 293, a sharply defined upper surface, and depth 8 614 m. Assume the observer is at the Earth’s equator so that the apparent path of the rising and setting Sun is perpendicular to the horizon.

A ray of light strikes the midpoint of one face of an equiangular (60°–60°–60°) glass prism (n = 1.5) at an angle of incidence of 40.8°. (a) Trace the path of the light ray through the glass, and find the angles of incidence and refraction at each surface.First surface: θincidence = ° θrefraction = ° Second surface: θincidence = ° θrefraction = ° (b) If a small fraction of light is also reflected at each surface, find the angles of reflection at the surfaces. θreflection = ° (first surface) θreflection = ° (second surface)

If a ray of light transitions from air into glass and we assume air has an index of refraction of n1=1.0 and θ1 is the angle of incidence, what variable should the slope of a graph of sin(θ1) as a function of sin(θ2) correspond to?