# What's the relation between angular resolution and distance

• Cocoleia
In summary, the conversation discusses the calculation of the angular resolution of a telescope and its relationship to distance. The individual used the formula θ=1.22λ/D to determine the angular resolution for a telescope with a diameter of 1m for visible light. However, they are unsure of the relationship between angular resolution and distance. A wiki article on angular resolution is suggested for further clarification. It is also mentioned that it is not possible to convert radians to meters. The question is then posed about the angular separation between two points on the moon when viewed from Earth.
Cocoleia

## Homework Statement

At first I needed to calculate the angular resolution of a telescope (diameter 1m, for visible light) so I used θ=1.22λ/D and got 4.88x10^-7 rad. Now I am asked: "If we wished to use this telescope to image the moon, what is the closest distance two objects can be to be distinguished by such a telescope?"
I don't understand what the relationship between angular resolution and distance is.

## Homework Equations

θ=1.22λ/D

Cocoleia said:
Is it just a matter of converting my answer to meters?
You cannot "convert" radians to metres.
If two points on the moon are distance x apart, what is their angular separation when viewed from Earth?

## 1. What is angular resolution?

Angular resolution is a measure of the smallest angle that can be resolved by a telescope or other optical instrument. It is a measure of the instrument's ability to distinguish between two closely spaced objects or features.

## 2. How is angular resolution related to distance?

The angular resolution of an instrument is inversely proportional to the distance between the observer and the object being observed. This means that as the distance increases, the angular resolution decreases. So, the farther away an object is, the harder it is to distinguish between its features.

## 3. What is the effect of increasing the distance on angular resolution?

As the distance between the observer and the object increases, the angular resolution decreases. This is because the angle between the observer's line of sight and the object's features becomes smaller, making it more difficult to distinguish between them.

## 4. How does the size of the aperture affect angular resolution?

The size of the aperture, or the opening through which light enters the instrument, directly affects the angular resolution. A larger aperture allows for more light to enter the instrument, increasing the angular resolution and allowing for better distinguishability between closely spaced objects or features.

## 5. Can angular resolution be improved by using a larger telescope?

Yes, using a larger telescope with a larger aperture can improve the angular resolution. This is because a larger aperture allows for more light to enter the instrument, resulting in a higher angular resolution and better distinguishability between closely spaced objects or features.

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