Question

An object is placed at the principal focus of a concave lens of focal length 10 cm. The image will be formed at___ cm, between the optical center and the focus of the lens on the same side of the object.

Answer 1

Correct Answer: 5

When dealing with lenses, the lens formula is given by: 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance. For a concave lens, the focal length is negative. Here, f = -10 cm, and the object is placed at the focus, hence u = -10 cm (object distances are also negative in lens equations).

Substituting in the lens formula: 1/(-10) = 1/v - 1/(-10). Simplifying gives:

1/(-10) = 1/v + 1/10

Bring similar terms together:

1/v = 1/(-10) - 1/10

1/v = -1/10 - 1/10 = -2/10 = -1/5

Thus, v = -5 cm. The negative sign confirms that the image is virtual and forms on the same side as the object.