Reflection at Curved Surfaces, Physics tutorial

Images Formed by Curved Mirrors:

We can determine nature and position of images created by curved mirrors with aid of ray diagrams drawn to scale. To do this, use of the facts given below:

i) The ray parallel to principal axis passes through principal focus after reflection as shown in (a) figure.

ii) The ray through center of curvature is reflected back along its path as shown in (b) figure

iii) As the corollary to (i), any ray through principal focus is reflected parallel to the principal axis shown in (c) Figure. Points to which reflected rays converge or from which they seem to diverge represent required image. Though, tracing of only two of the rays will allow us to determine position of image.

 1294_Images Formed by Curved Mirrors.jpg

Image Formed by a Concave Mirror When the Object is Placed Beyond Centre of Curvature:

2416_Image Formed by a Concave Mirror.jpg

Figure given above shows ray diagram for Image formed by the concave mirror when object is placed beyond the center of curvature and OP represents the object, IQ represents image. F and C respectively represent the Principal focus and the center of the curvature of the mirror.

It shows that image formed is inverted (i.e., in opposite direction to object). Image is also diminished (i.e., smaller than object) and it happens to right of the center of curvature C. At last, image is real, as it can be received on screen.

Image Formed by the Concave Mirror when Object is Placed between Center of Curvature C and Principal Focus F:

1423_Image formed by a concave mirror1.jpg

It shows ray diagram for image formed by the concave mirror when object is placed between center of curvature C and principal focus F.

The figure given above suggests that image formed by concave mirror has characteristics given below:

i) It is real;

ii) It is magnified, i.e., larger than the object;

iii) It occurs after C (to left of C); and

iv) it is inverted.

Image Formed by a Concave Mirror when the Object is between the Principal Focus F and the Mirror:

It shows the ray diagram of image formed by concave mirror when object lies between the mirror and principal focus F.

1520_Image formed by a concave mirror2.jpg

The figure suggests that the image formed is behind the mirrors. Therefore, it is virtual because it cannot be received on the screen.

The Mirror Formula:

It is a distance of object from mirror is called as object distance. This is generally signified by letter u. Likewise, distance between image and mirror is called as image distance, this is usually signified by letter v, also one may not require to find out u or v by construction as it has been experimentally found, that there is mathematical relationship connecting the parameters (without proof). Mathematical relationship is provided as:

1/v + 1/u = 1/f

Where f is the focal length.

Magnification:

In the day to day language, magnification is a degree of enlargement or reduction of size of the object through it image formed.

Magnification is mathematically signified by M.

M = Height of image/Height of object

This can also be signified in terms of image distance of mirror v and object distance u from mirror. Mathematically it can be stated as:

M - Image distance/object distance

I.e. M = v/u

The real image is considered as having positive value, while the virtual image is regarded as having negative value. This convention is usually borne in mind in application of mirror formula. This signifies that distances for real objects and images are regarded as positive while distance for virtual objects or images are considered to be negative. Also, focal length for the concave mirror is usually regarded as positive while that of the convex mirror is considered as negative value.

Convex mirror:

1750_Convex mirror.jpg

It shows ray diagram for formation of the image by the convex mirror. OP is an object and IQ is an image. As usual, ray PA that is parallel to principal axis of mirror, is reflected from surface of the mirror at A as if it is coming from F. Also, ray PB which is directed from top of the object towards center of curvature (C) of mirror is reflected back along same path as if it is coming from C. Therefore, intersection of two rays gives rise to formation of image IQ. It shows that image formed by convex mirror is

i) Upright

ii) Formed behind the mirror; therefore it is virtual;

iii) Diminished, that is, smaller than the object.

It is essential to note that features of image defined above are true for convex mirror, irrespective of where object is placed in front of the mirror. Therefore, convex mirror is said to have a very wide field of view. Therefore, as image formed by the convex mirror is erect, convex mirror is always use in motor vehicle as side mirror.

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