A concave mirror is kept as shown in figure. Its principal axis coincides with the x-axis. A real object is moving towards the pole of the mirror starting from the −\[\infty \] . In which region image will never form –

A). Between -\[\infty \] and C
B). Between C and F
C). Between F and P
D). Between P and +\[\infty \]

Hint: Here the image of the object will not be formed in two regions. The region between C and F and F and P in most cases will produce an image. An image will be formed at the focus when the object is at infinity.

Complete answer:
Image will never be formed in the region between -\[\infty \] and C and the region between P and +\[\infty \]. At \[\infty \] the image will be formed at the focus, F and the image will be highly diminished. Beyond C the image will be formed between F and C and will be diminished. At C the image will be formed at C itself and will be of the same size. When the object is beyond C and F the position of the image will be beyond C and it will be enlarged. When the object is at F, the image will be formed at infinity and will be highly enlarged. When the object is between F and P, the image will be behind the mirror, it will be enlarged and the image will be erect and virtual.

Options A and D are the correct answers.

Note:
The concave mirror creates both actual and virtual images. A virtual and magnified signal is produced when the object is placed very close to the mirror. When the object is outside of C for concave mirrors, the image will be between C and F, inverted and diminished.