What are sign conversions for object, image,focal length of concave and convex lens and for telescope while solving ray optics problems

In ray optics, the sign conventions are very important to understand the nature of the image formed, the position of the object, and the focal length of the lens. Here are the sign conventions for object, image, and focal length for concave and convex lenses:

1. Object Distance (u):

   • The object is always placed to the left of the lens in ray diagrams. Therefore, the object distance is always negative.

2. Image Distance (v):

   • For a Convex Lens: If the image is formed on the right side of the lens (opposite to the side of the object), the image distance is taken as positive. If the image is formed on the same side as the object, the image distance is negative.
   • For a Concave Lens: The image is always formed on the same side as the object, so the image distance is always negative.

3. Focal Length (f):

   • For a Convex Lens: The focus is on the right side of the lens, so the focal length is positive.
   • For a Concave Lens: The focus is on the same side as the object, so the focal length is negative.

For a telescope, the sign conventions are a bit different:

1. Object Distance: The object is considered to be at an infinite distance, so the object distance is positive.

2. Image Distance: The image is formed at the focus of the telescope, so the image distance is negative.

3. Focal Length: The focal length of the objective lens is positive, while the focal length of the eyepiece is negative.

Remember, these conventions are based on the Cartesian coordinate system. The origin is at the optical center of the lens, the positive direction is to the right, and the negative direction is to the left.