The earth is 149.600.000 km away from the sun and the speed of light is 299 792.458 kilometres / second, therefore, it would take sunlight, on average, 8 minutes and 20 seconds to reach earth.
Now, imagine the following scenario, which I think we can all relate to: you are at the beach and the sun is shining, what a wonderful day! But no, suddenly clouds appear and bye-bye good time, because the sun gets in the clouds. Some time passes, and you can see the sun coming out of the clouds, and the second this happens, you feel the warm embrace of our extraordinary favourite star.
My question is, from what I said in the beginning, sunlight travels to earth in 8 minutes and 20 seconds, however, we immediately feel it when the sun gets out of the clouds, why is that? Because from what I can see, it should take 8 minutes and 20 seconds
Best Answer
Sunlight is hitting earth at all times. If clouds block the sunlight that happens at a height $h$ above earth's surface. If clouds let the sunlight pass, there is already light just beyond the cloud (which started at the sun some 8 min earlier). It is not that the light has to travel all the way from the sun when that happens.
You will see the sun coming out of the clouds, only a time $h/c$ after the clouds have given way to the sun, because in order for you to see, light has to travel from the clouds to you, which it does at the speed of light. Similarly the warmth (being carried by photons/light) has to travel the same distance and is travelling at the same speed.
Or said differently, the warm embrace/heat/energy that you feel travels at the same speed as the image you see with your eyes. That's why it does not matter whether the clouds are at $h=2~km$ or whether the blocking occurs close to the sun.
If the blocking occurred close to the sun, you would see the opening of the blocking ca. 8 minutes after it happened, but you would also feel it 8 min after it happened. Thus you would experience both at the same time.
An analogy:
Imagine a car standing at a tunnel entrance that is blocked. You are standing at the opposite end of the tunnel. Now the road is opened and the car drives through the tunnel towards you. The car reaches you ("warmth") at the same moment that you receive the information that the tunnel is not blocked anymore. It does not matter how long the tunnel is or how fast the car is driving.