So you should now be able to
identify different components of a concave and convex mirror,
like Pole, Principal Focus, Center of Curvature, Focal Length etc.
Also you should now have a clear conception
about the reflection rules like Rule 1, Rule 2, Rule 3 and Rule 4
for both types of spherical mirror.
This page studies the nature, size and location of a formed image
reflected by a concave as well as a convex mirror.
Real and virtual image
Let us check first what are actual and virtual rays.
A virtual ray has no actual existence, it is imagined to be there.
Such rays appear to be travelling through an imaginary path.
They cannot be projected on a screen or wall.
In case of a spherical mirror, they are the result of
actual diverging rays, and seem to be behind the mirror.
On the other hand, an actual ray has real existance, and
can be projected on a screen or wall. They are the actual converging rays,
and they travel in front of the mirror.
In the world of Optics, a real image is said to form when
reflected rays actually meet at a point. These reflected rays
are actual, not virtual. So the formed image is also real, not virtual.
Virtual images are the result of imaginary meeting of virtual rays.
A virtual image always forms behind the mirror.
Plane and convex mirrors create virtual images.
Concave mirrors create real images,
except when an
object is placed in between the Principal Focus and the Pole. In that case, a virtual image is formed behind the mirror.
Having the above facts in our mind, let us check
six cases of image formation for concave mirrors,
and two cases for convex mirrors.
Concave Mirror Image Formation
Concave mirror: Object(the Sun) at infinity
Case 1 of 6
When some incident rays, originated at infinity and
each parallel to the Principal Axis, fall on a concave mirror,
they reflect back travelling through the Principal Focus of the mirror.
An image of the object (where the rays are coming from, for example, the Sun)
is formed at the focal point
which is the meeting point of the reflected rays.
In this case, the reflected rays are converging to a point;
so concave mirrors are also called converging mirrors.
Such phenomenon produces a point-sized real image
at the Principal Focus of the mirror.
Here, the Sun is the source of light, so light energy gathered
at the focal point will produce tremendous heat, enough to cook food
keeping a bowl at the right place.
Concave mirror: Object at beyond Center of Curvature
Case 2 of 6
Three incident rays, blue, red and green are falling on the concave mirror.
The blue incident ray travels parallel to the Principal Axis;
so the reflected ray passes through the Principal Focus
[Rule 1]
The red incident ray passes through the Principal Focus;
so the reflected ray travels parallel to the Principal Axis.
This is inverse of the above rule.
[Rule 2]
The green incident ray passes through the Center of Curvature C;
so the reflected ray travels back through the same path;
[Rule 3]
When an object is placed at beyond the Center of Curvature C,
for a concave mirror, image is formed between the
Center of Curvature and the Principal Focus.
Nature of formed image will be REAL, DIMINISHED and INVERTED.
Concave mirror: Object at Center of Curvature
Case 3 of 6
Three incident rays, blue, red and green are falling on the concave mirror.
The blue incident ray travels parallel to the Principal Axis;
so the reflected ray passes through the Principal Focus.
The red incident ray passes through the Principal Focus;
so the reflected ray travels parallel to the Principal Axis.
The green incident ray passes through the Center of Curvature C;
so the reflected ray travels back through the same path.
When an object is placed at the Center of Curvature C,
for a concave mirror, image is formed at the same location.
Nature of the image will be REAL, of SAME SIZE and INVERTED.
Concave mirror: Object between Center of Curvature and Principal Focus
Case 4 of 6
Three incident rays, blue, red and green are falling on the concave mirror.
The blue incident ray follows Rule 1. The red one follows Rule 2, while the
green one follows Rule 3.
The object is placed between the Center of Curvature C and Principal Focus F.
Image is formed beyond the Center of Curvature C.
Nature of image will be REAL, MAGNIFIED and INVERTED.
Concave mirror: Object on the Principal Focus F
Case 5 of 6
Two incident rays, green and red, are falling on the concave mirror.
The green incident ray travels parallel to the Principal Axis;
so the reflected ray passes through the Principal Focus [following Rule 1].
The red incident ray seems to be travelling through the Center of Curvature C;
so the reflected ray travels back through the same incident path; [following Rule 3].
The object is placed on Principal Focus F.
Since the two reflected rays are parallel,
they will never meet. So we assume that the image will form at INFINITY.
Nature of the image will be REAL, HIGHLY ENLARGED and INVERTED.
Concave mirror: Object in between Principal Focus and Pole
Case 6 of 6
Rules are as per the previous case,
we just change the position of the object,
and place it in between Principal Focus F and Pole P.
Image is formed behind the mirror.
Nature of image is VIRTUAL, ENLARGED and ERECT.
This is the only case of a concave mirror when a
virtual and erect image
is formed behind the mirror. In all other five cases
real and inverted image
was formed in front of the mirror.
Convex Mirror Image Formation
Convex mirror: Object(the Sun) at infinity
Case 1 of 2
When incident rays are parallel to the Principal Axis, the reflected rays travel
back as if coming from the Principal Focus.
An image is formed at the Principal Focus behind the mirror.
In this case, the reflected rays are diverging;
so convex mirrors are also caled diverging mirrors.
Please compare this with Case 1 of concave mirror.
In the former, rays converged and met at the Principal Focus.
In case of convex mirror, actual reflected rays diverge, so they never meet.
Each parallel ray will diverge in such way, that,
it appears to be coming from the Principal Focus.
For a convex mirror, the Principal Focus or the Focal Point
lies behind the mirror, i.e., on the non-reflecting side.
So, the image is virtual in nature.
So for a convex mirror, if an object is at infinity,
the image will be at Principal Focus.
Nature of the formed image will be VIRTUAL, POINT-SIZED and ERECT.
Convex mirror: Object in between infinity and Pole
Case 2 of 2
Place an object in between infinity and the Pole of the convex mirror.
Three incident rays, blue, red and green are falling on the convex mirror.
The blue incident ray travels parallel to the Principal Axis;
so the reflected ray travels back as if coming from the Principal Focus.
The red incident ray travels as if it will pass through the Center of Curvature C;
so the reflected ray travels back through the same path.
The green reflected ray also follows Rule 3 like the red one.
As a result, we again get a virtual image behind the mirror,
diminished in size, and erect in nature.
Summary: Image Formation
Concave 01 -
Object at infinity
Image is real, point-sized at PF.
Concave 02 -
Object at beyond the Center of Curvature
Image is real, diminished and inverted, between CoC & PF.
Concave 03 -
Object at the CoC
Image is real, of same size, inverted at CoC.
Concave 04 -
Object between CoC and PF
Image is real, magnified and inverted at beyond CoC.
Concave 05 -
Object on PF
Image is real, highly enlarged, inverted at infinity.
Concave 06 -
Object between PF & Pole
Image is virtual, magnified, erect behind the mirror.
Convex 01 -
Object at infinity
Image is virtual, point-sized at PF.
Convex 02 -
Object in between infinity and Pole
Image is virtual, diminished, erect, behind the mirror between Pole & PF
