Given below are two statements :
Statement (I) : When an object is placed at the centre of curvature of a concave lens, image is formed at the centre of curvature of the lens on the other side.
Statement (II) : Concave lens always forms a virtual and erect image.
In the light of the above statements, choose the correct answer from the options given below :

Solution

Physics sir · 4 steps

Put u = -2|f| into the lens formula with f negative, and the image lands on the same side, not at 2F.

1. Set up signs. For a concave lens the focal length is negative, f = -|f|. Treat the centre of curvature as the point at distance 2|f|, so a real object there has u = -2|f|.

   1/v = 1/f + 1/u = -1/|f| - 1/2|f| = -3/2|f|

2. Statement I. This gives v = -2/3|f|. The negative sign puts the image on the same side as the object, between the lens and its focus. It is not at the centre of curvature on the other side, so Statement I is false.
3. Statement II. For any real object, 1/v = 1/f + 1/u has two negative terms on the right, so v is always negative. The image is always virtual, and magnification m = v/u is positive and less than 1, so it is erect and diminished. Statement II is true.
4. So. Statement I is false and Statement II is true, which is option (a).

The idea to keep. Object at 2F giving an image at 2F on the other side is a convex lens result. A concave lens with a real object always gives a virtual, erect, diminished image between the lens and F.

Answer from the NTA final answer key. Solution by PrepWiser.