Question

the radius of carvature of a concave morror is 30m .where should the object lee placed from the mirror so as to form its image at infinity?draw ray daigramto justify your answer

Answer 1

When an object is placed at infinity, the rays coming from it are parallel to each other. Let us consider two rays, one striking the mirror at its pole and the other passing through the center of curvature. The ray which is incident at the pole gets reflected according to the law of reflection and the second ray which passes through the center of curvature of the mirror retraces its path. These rays after reflection form an image at the focus. The image formed is real, inverted and diminished.

The image is

At F
Real
Inverted
Diminished


Concave Mirror Image
When the Object is Placed beyond C :

The two rays which are considered to obtain the image are :

A ray passing through the center of curvature
A ray parallel to the principal axis. The ray passing through the center of curvature retraces its path and the ray which is parallel to the principal axis passes through the focus after reflection. These rays after reflection meet at a point between C and F. The image is inverted, real and diminished
The image is

Between C and F
Real
Inverted
Diminished


Concave Mirror Diagram
When the Object is Placed at the Center of Curvature:
Consider the two rays, one parallel to the principal axis and the other passing through the focus. The ray of light which is parallel to the principal axis passes through the focus after reflection. The other ray passing through the focus after reflection emerges parallel to the axis. After reflection these rays meet at the center of curvature to form an inverted image, which is real and of the same size as the object.

The image is

At C
Real
Inverted
Same size as object


Concave Mirror Images
When the Object is between C and F :
Here we consider a ray of light which is parallel to the principal axis and another ray passing through the focus. The ray which is parallel to the principal axis passes through the principal focus and the ray which passes through the focus after reflection emerges parallel to the principal axis. The reflected rays meet at a point beyond C and the image is real, inverted and magnified.

The image is

Beyond C
Real
Inverted
Magnified


Image in Concave Mirror
When the Object is between C and F :
Let us consider a ray of light which is parallel to the principal axis and another ray passing through the center of curvature. The ray which is parallel to the principal axis passes through the focus and the ray which passes through the center of curvature retraces its path. The reflected rays are parallel to each other, and would meet only at infinity i.e., the image is formed at infinity and it is a real, inverted, enlarged image of the object.

The image is

At infinity
Real
Inverted
Magnified