Question

In Fig. 34-26, stick figure Ostands in front of a spherical mirrorthat is mounted within the boxed region;the central axis through themirror is shown. The four stick figures ${\mathit{I}}_{\mathbf{1}}$to ${\mathit{I}}_{\mathbf{4}}$suggest general locationsand orientations for the images that might be produced by themirror. (The figures are onlysketched in; neither their heightsnor their distances from the mirror are drawn to scale.) (a) Whichof the stick figures could not possibly represent images? Of thepossible images, (b) which would be due to a concave mirror, (c)which would be due to a convex mirror, (d) which would be virtual,and (e) which would involve negative magnification?

Short answer

(a) The stick figures that could not possibly represent images are $I_1,I_2$and$I_3$.

(b) The images due to the concave mirror are$I_2$ and$I_3$.

(c) $I_3$represents the image of a convex mirror.

(d) Image$I_3$ is the only possible case of virtual image.

(e) role="math" localid="1662992456509" $I_2$would give negative magnification.

Step-by-step solution

Description of the images formed by the various mirrors

The images formed by the concave mirrors can be both real and virtual depending upon the position of the object. The image formed by a convex mirror is upright, virtual, and diminished.

A virtual image is an image obtained with the help of an optical system when light rays from a source do not cross to form an image.

The magnification of a mirror is obtained by dividing the height of the obtained image by the height of the thing that is appeared in the mirror.

(a) Determination of the possible case of images for the stick figure

As per the concept, the concave mirror can produce upright, inverted real images and upright virtual images, while the convex mirror produces upright virtual images.

Thus, $I_1,I_2$and $I_3$are all the possible image figures for the given object except the image $I_4$.

(b) Determination of the image due to the concave mirror

In the case of the concave mirror, the images can be both real and inverted. For a given case of an object at infinity, the image formed will be given by$I_1$at the focal point of the mirror. But here, the object is at a definite distance from the mirror.

Thus, the images due to the concave mirror are $I_2$and $I_3$.

(c) Determination of the image due to convex mirror

As per the given concept, the image is upright and at the opposite side of the mirror.

Thus, $I_3$represents the image of a convex mirror

(d) Determination of the virtual image

As per the concept, the virtual image is formed behind the mirror.

Thus, image $I_3$is the only possible case of virtual image.

(e) Determination of the image that would give negative magnification

As it a case of spherical mirror, thus, the image that is formed in the side of object and is inverted would give negative magnification.

Thus, $I_2$would give negative magnification.