Question

Give the ray diagrams indicating the position, size and nature of the image formed by a convex mirror when an object is kept

(a) at infinity

(b) between pole and infinity

Describe the formation of images in both the cases.

Accepted Answer

The spherical mirror in which the reflection of light takes place at the bulging surface (convex surface) is called a convex mirror. The other surface of the convex spherical mirror is opaque and non-reflecting.

The following diagram represents the image formed by a convex mirror when an object is kept at infinity.

In the above ray diagram, the object $A B$ is at a very, large distance say at infinity. Since the object is it very far distance, it cannot be shown in the ray diagram. The two rays from $A$ , $A P$ and $A Q$ parallel to each other, but are inclined to principal axis at an angle, the ray $A P$ gets reflected as $P X$ and the ray $A Q$ gets reflected as $Q Y$ . When these two reflected rays $P X$ and $Q Y$ are produced backwards by the dotted line, they meet at $A ’$ at focus of convex mirror. Thus, $A ’$ is the virtual image of object $A$ . Drawing a perpendicular to the principal axis of the mirror $M N$ , we get $A ’ B ’$ as the virtual image of $A B$ . Thus, we can conclude that when an object is at infinity, its image will be virtual and erect, highly diminished and formed behind the mirror at the focus.

The following diagram represents the image formed by a convex mirror when an object is kept between pole and infinity. The pole is the centre of the spherical mirror, and it is denoted by the letter $P$ .

In the ray diagram, the object $A B$ is placed anywhere between infinity and the pole of a convex mirror $M N$ . When a ray of light from $A$ falls on the mirror along $A X$ in the direction parallel to the principal axis of the convex mirror, it gets reflected along $X Y$ .

Now, according to the first rule of image formation by a convex mirror, when a ray of light coming parallel to the principal axis of a convex mirror, it appears to be coming from its focus after reflection from the convex mirror. So reflected ray $X Y$ appears to be coming from focus $F$ of the convex mirror. Now, another ray of light from $A$ falls on the mirror along $A E$ , towards the centre of curvature $C$ of the convex mirror, retraces its path of reflection at $E$ . When we produce the reflected ray $E A$ backwards the reflected ray $E A$ appears to be coming from centre of curvature $C$ , of the convex mirror. The two reflected ray $X Y$ and $E A$ meets at $A ’$ which is the image of object $A$ . When a perpendicular from $A ’$ is drawn to the principal axis of the mirror $M N$ , we get $A ’ B ’$ as the image of $A B$ at the back of the convex mirror.

Thus, we can conclude that when an object is placed anywhere between the infinity and pole of the convex mirror, its image will be virtual as it cannot be captured on the screen and erect, diminished and formed between $P$ and $F$ behind the mirror.

Give the ray diagrams indicating the position, size and nature of the image formed by a convex mirror when an object is kept

(a) at infinity

(b) between pole and infinity

Describe the formation of images in both the cases.

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