Can somebody explain what is happening here? (sunlight refracting in Earth's atmosphere)

[tellmesomething]

Homework Statement

A light from the sun enters the atmosphere, it refracts due to the small difference between the speed of lights in air and vaccum. The optical length of the day is defined as the time interval between the instant when the top of the sun is just visibly observed above the horizon to the instant at which the top of the sun disappears below the horizon. The geometric length of the day is defined as the time interval bewteen the instant when a geometric straight line drawn from the observer to the top of the sun just clears the horizon to the instant at which this line just dips below the horizon?

Relevant Equations

None

I honestly do not understand which one is referring to which one, the optical length states that the time interval between the instant when the top of the sun is just "visibly observed" above the horizon to the instant at which the top of the sun just disappears below the horizon. The sun that is "observed" Is the virtual image as seen in the diagram.

But geometric length is defined as the time interval between the instant when a geometric line is drawn from the observer to the top of the sun just clears the horizon to the instant at which this line dips below the horizon. If you see it like this it must mean the "actual sun"' when it comes up the horizon and not the virtual image so doesn't it make both the time intervals equal?

The answer given is A

 

[Steve4Physics]

For simplicity, consider yourself on the equator.

At sunrise, can you see the upper edge of the sun before it is geometrically lined up with the horizon and you?

At sunset, the upper edge of the sun is what was the lower edge of the sun at sunrise,

At sunset, can you see the upper edge of the sun after it is geometrically lined up with the horizon and you?

 

[haruspex]

Your diagram seems to show the sun going around clockwise relative to the Earth, so I guess we are looking down on the N pole, with W on the right and E on the left.
The upper image of the sun on the right shows where you would see it set if no refraction, and the lower right where it is when you do see it set. Which is later?

 

[tellmesomething]

For simplicity, consider yourself on the equator.

At sunrise, can you see the upper edge of the sun before it is geometrically lined up with the horizon and you?

At sunset, the upper edge of the sun is what was the lower edge of the sun at sunrise,

At sunset, can you see the upper edge of the sun after it is geometrically lined up with the horizon and you?

Yes I can stil see the upper edge after it is geometrically lined up with the horizon. So like the day starts earlier and ends later for us observers? Hence the time interval is longer?

 

[tellmesomething]

Your diagram seems to show the sun going around clockwise relative to the Earth, so I guess we are looking down on the N pole, with W on the right and E on the left.
The upper image of the sun on the right shows where you would see it set if no refraction, and the lower right where it is when you do see it set. Which is later?

The upper image of the sun on the right

 

[Steve4Physics]

Yes I can stil see the upper edge after it is geometrically lined up with the horizon. So like the day starts earlier and ends later for us observers? Hence the time interval is longer?

Yes, spot-on.
Well, almost spot-on! See post #7.

 

[Steve4Physics]

@tellmesomething, just noticed an issue with what you wrote (sorry - I should have read it more carefully).

Yes I can stil see the upper edge after it is geometrically lined up with the horizon.

That's only true at sunset.

At sunrise, you can see the upper edge before it is geometrically lined up with the horizon.

So like the day starts earlier and ends later for us observers? Hence the time interval is longer?

Yes.

 

[haruspex]

The upper image of the sun on the right

In your diagram the sun is going clockwise, so it is descending on the right. In which position is it later, upper right or lower right?

 

[tellmesomething]

In your diagram the sun is going clockwise, so it is descending on the right. In which position is it later, upper right or lower right?

The sun is physically on the lower right but we see it on the upper right right during sunset...its virtual image is what we see and in our pov it stays for longer..

 

[tellmesomething]

@tellmesomething, just noticed an issue with what you wrote (sorry - I should have read it more carefully).


That's only true at sunset.

At sunrise, you can see the upper edge before it is geometrically lined up with the horizon.


Yes

Yes, since you specifically asked in post #2 about sunset so that's what I replied to..

At sunset, can you see the upper edge of the sun after it is geometrically lined up with the horizon and you?

 

[haruspex]

The sun is physically on the lower right but we see it on the upper right right during sunset...its virtual image is what we see and in our pov it stays for longer..

Right.

 

[Steve4Physics]

Yes, since you specifically asked in post #2 about sunset so that's what I replied to..

In Post #2 I asked two separate questions - one specifically about sunrise and one specifically about sunset. Sorry to be picky.

 

[tellmesomething]

In Post #2 I asked two separate questions - one specifically about sunrise and one specifically about sunset. Sorry to be picky.

Oh i missed that sorry just noticed. Anyways thankyou for helping me understand it. ☺