 # Image Formation by Spherical Mirrors

Have you ever gone camping in the night or have walked inside a cave? Whenever its dark, you must have used a torch to show you the right path. Why not a candle instead? Well, torches have special spherical mirrors which make the light focused in the direction you want to go. Let’s find out the mechanism involved in the image formation by spherical mirrors…

### Suggested Videos        ## Ray Diagrams

Ray diagrams are used to depict the image formation by tracing the path of light rays i.e. incident rays and reflected rays. They are drawn in order for anyone to view a point on the image of an object. These ray diagrams depend on the position of the object.

### General rules for image formation using ray diagrams:

• Any ray of light that passes through the mirror, is always parallel to the principal axis.
• Any ray of light that passes through the mirror always passes through the principal focus (f) of the mirror after reflection.
• A ray of light passing through the center of curvature of any mirror is reflected back along the same path.
• Any incident ray which isn’t parallel to the principal axis is also reflected diagonally and the incident ray and the reflected ray always follow the laws of reflection i.e. the angles formed by these rays are equal to each other. ### Ray Diagrams for a Concave Mirror

For a concave mirror, there are six possible positions where the object can be positioned and an image is formed:

#### a. Object is positioned at infinity When the object is placed at infinity, rays PQ and RS parallel to the axis are reflected from points Q and S respectively. Rays PQ and RS intersect each other and get converged at the principal focus (f). And since when the object is placed at infinity, the properties of the images formed are highly diminished, point sized and real and inverted.

#### b. Object is positioned between infinity and center of curvature(c) Here the object MN is placed between infinity and center of curvature (c) of a concave mirror, then a ray MP parallel to the principal axis and another ray MQ that pass through the center of curvature(c) intersect each other at M’ after reflection between focus (f) and center of curvature (c). Therefore the properties of the images formed here are that the image formation is between principal focus (f) and center of curvature (c), the image formed is diminished and real and inverted.

#### c. Object is positioned at Center of Curvature (c) When the object MN is placed the at the center of curvature (c), then a ray MP parallel to the principal axis and another ray MQ that passes through the principal focus (f) after reflection, intersect each other at point M’ right below where the object MN is positioned. Hence the properties of the images formed in this case are that image is formed at the center of curvature, the image is the same size as the object and images are real and inverted.

#### d. Object is positioned between the center of curvature (c) and principal focus (f) Object MN is placed between the center of curvature (c) and principal focus (f), then the ray MP parallel to the principal axis and another ray MQ passing through principal focus (f) intersect each other beyond the center of curvature (c) at point M’. Hence the properties of the images formed here are that the image is formed beyond the center of curvature (c), and the image is real and inverted.

#### e. Object is positioned at principal focus (f) Object MN is positioned at the principal focus (f), then ray MP parallel to the principal axis passes through principal focus (f) giving the reflected ray PS. Second ray MQ that passes through the center of curvature is reflected along the same path giving the reflected ray QR. Here, since the rays, PS and QR become parallel to each other and therefore the image formation is at infinity. Here the properties of the images formed are highly enlarged images and real and inverted images.

#### f. Object is positioned between principal focus (f) and pole (p) Object MN is positioned between principal focus (f) and pole (p), then the ray MP parallel to principal axis passes through principal focus (f) giving the reflected ray PS and the second ray MQ that passes through the center of curvature is reflected along the same path giving the reflected ray QR.

Now, since the reflected rays PS and QR are diverging away hence cannot intersect each other, hence reflected rays PS and QR are extended behind the mirror by dotted lines. In doing so, rays PS and QR appear to intersect each other at point M’ backwards. Therefore, the properties of the images formed here are formed behind the mirror, images are highly enlarged, images are virtual and erect.

### Ray Diagrams for a Convex Mirror

In case, of a convex mirror, there are only two possible positions where the object can be positioned and an image can be formed.

a. Object is positioned at Infinity When the object is at infinity, the rays MN and PX that are parallel to the principal axis (f) are divergent in the direction NZ and XY respectively; after getting reflected from the convex mirror. The diverged rays NZ and XY are extended behind the mirror, where they intersect each other at the principal focus (f). Hence, in this case, the properties of the images formed are formed at the principal focus (f) behind the mirror and are highly diminished, the images are virtual and erect.

#### b. Object is positioned between the pole (p) and the principal focus (f) When the object MN is placed between pole (p) and infinity, a ray MC that starts from point M of the object MN that’s running parallel to the principal axis is reflected along CY. On extending behind the mirror, CY appears to come from principal focus (f) and another ray MD from point M of the object MN that goes towards the center of curvature is reflected along DM. The two rays, CY and DM are diverging rays and when extended behind the mirror, they appear to intersect each other at point M’.

Therefore, the properties of the images formed here are formed behind the mirror, between the pole and principal focus (f), the images are diminished and are virtual and erect.

## Solved Example for You

Q: The value of the focal length of the lens is equal to the value of the image distance when the rays are:

a. Passing through the optic center

b. Parallel to the principal axis

c. Passing through the focus

d. In all the above cases

Sol: b. Parallel to the Principal axis According to the rule of ray optics, all the rays parallel to the principal axis must pass through the focus of the lens after getting refracted from that lens as shown in the figure. Thus, in this case, the image formation is at the focus of the lens and hence the value of image distance is equal to the focal length of the lens.

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