Let's analyze the given statements regarding the effects of Earth's curvature and atmospheric refraction on the apparent position of distant objects.

Understanding Earth's Curvature and Object Position

Statement (i) says: The effect of the curvature of the earth is to cause an object to appear lower.

When we observe a distant object on Earth's surface, we are looking along a line of sight. Because the Earth is round (it curves away from us), the surface dips down relative to a straight line from our observation point. Imagine standing on a beach and watching a ship sail away. As it gets further, the hull disappears first, and finally, only the mast is visible before it disappears completely below the horizon. This happens because the curve of the Earth hides the lower parts of the ship.

Therefore, the effect of Earth's curvature is that a distant object's true position is effectively lower than our line of sight if we were on a flat plane extending from our position. This causes the object to appear lower than its actual height relative to our horizon line, and in extreme cases, it might even be hidden below the horizon.

So, Statement (i) is correct.

Understanding Atmospheric Refraction and Object Position

Statement (ii) says: The effect of refraction is to cause an object to appear higher.

Atmospheric refraction is the bending of light rays as they pass through the Earth's atmosphere. The atmosphere is denser near the Earth's surface and becomes less dense at higher altitudes. Light travels slower in denser air. As light rays from a distant object travel towards an observer, they pass through layers of air with varying densities. This causes the light rays to bend downwards, towards the denser air near the surface.

Our brain assumes that light travels in straight lines. So, when we see an object, we perceive it as being located along the straight line tangent to the light ray as it enters our eye. Since the light ray from a distant object bends downwards towards the observer, the tangent line (our line of sight) points slightly upwards relative to the object's true position. This makes the object appear to be higher than it actually is.

This effect is particularly noticeable for objects near the horizon, such as the sun or moon, which can appear flattened or distorted due to refraction.

So, Statement (ii) is also correct.

Conclusion based on Statement Analysis

Both Statement (i) and Statement (ii) accurately describe the effects they mention:

• Earth's curvature makes objects appear lower by hiding parts below the horizon or reducing their apparent elevation angle.
• Atmospheric refraction makes objects appear higher by bending light rays downwards, causing our line of sight to be elevated relative to the true position.

Therefore, both statements are correct.

Let's look at the options:

1. Only (i) is correct - Incorrect, as (ii) is also correct.
2. Both (i) and (ii) are correct - Correct, as both statements are accurate.
3. Only (ii) is correct - Incorrect, as (i) is also correct.
4. (i) is correct and (ii) is incorrect - Incorrect, as both are correct.

Revision Table: Effects on Apparent Position

Additional Information: Combined Effects

In surveying and astronomy, both the effects of Earth's curvature and atmospheric refraction are significant and often need to be accounted for. While curvature makes objects appear lower, refraction makes them appear higher. These two effects often work in opposition.

For typical terrestrial observations over moderate distances, the effect of curvature is generally larger than the effect of standard atmospheric refraction. However, the exact amount of refraction varies depending on atmospheric conditions like temperature, pressure, and humidity gradients. This variability makes precise calculations challenging.

In practice, corrections are applied in activities like surveying, navigation, and astronomical observations to account for these natural phenomena and determine the true position or elevation of objects.