Concave lenses are characterized by their curved-inward shape. When light rays pass through a concave lens, they diverge (spread out). Here are some key points about concave lenses:

1. Focal Length:

   • The focal length of a concave lens is always negative.
   • It represents the distance from the lens to the point where parallel rays converge (or appear to converge) after passing through the lens.
   • In your case, the focal length is given as 10 cm.

2. Image Formation:

   • When an object is placed in front of a concave lens, the following scenarios can occur:
     • If the object is at infinity (very far away), a virtual, highly diminished image is formed at the focus.
     • If the object is beyond the center of curvature, a real, diminished image is formed between the center of curvature and the focus.
     • If the object is at the center of curvature, a real, same-sized image is formed at the other center of curvature.
     • If the object is between the center of curvature and the focus, a real, enlarged image is formed behind the center of curvature.
     • If the object is at the focus itself, a real, highly enlarged image is formed at infinity.
     • If the object is between the focus and the optical center, a virtual, enlarged image is formed.

3. Lens Formula:

   • The lens formula relates the object distance ((u)), image distance ((v)), and focal length ((f)) of a lens: [ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} ]
   • Given that the focal length ((f)) of your concave lens is -15 cm and the image distance ((v)) is -10 cm, we can find the object distance ((u)): [ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} ] [ \frac{1}{(-15)} = \frac{1}{(-10)} - \frac{1}{u} ] Solving for (u): [ \frac{1}{u} = \frac{1}{10} - \frac{1}{15} ] [ \frac{1}{u} = \frac{2}{30} ] [ u = -30 , \text{cm} ]