Light - Part VI

Images by convex mirrors
To find out how images are formed with the convex mirrors, we have to consider certain rules as regards to rays of lights coming from different directions on the surface of the mirror and how they get reflected.

Second rule :  A ray of light passing through the centre of curvature C, is reflected back, un-deviated along the same path.

Line AEC gets reflected along the same line.

It should be noted that in case of convex mirrors, C and F are behind the mirror surface.

Unlike the different cases seen in case of concave mirrors, the images formed by convex mirrors are always the same!

Consider Fig 1 again. Let the candle AB be placed at any distance from P. Two rays from A, one AD parallel to CP and another AE passing virtually from C. The parallel ray of light will appear to converge at F. The ray AEC will be reflected back to CA’EA. The image of A will form at the intersection of the two rays, that is at A’. The ray of light from B will be reflected along the same line. Thus B’ is on line BPFC. The image of the candle AB is A’B’.

Thus whatever the position of the object in front of a convex mirror, the image is always :

• Formed behind the mirror between the pole P and the focus F.

• The image is erect and virtual

• The image is diminished and reduced in size.

A convex mirror is used as a rear view mirror in cars and buses, because it lets you see a large distance and a wide field of view in a concise manner.

Mirror formula and magnification
To find out the focal length of a mirror, a formula is used. But before we find the mirror formula, some sign conventions are to be strictly followed.

Sign conventions :
1. All distances are measured from the pole P.
2. Distances measured in the direction of the incident light rays are taken as positive.
3. Distances measured in the direction opposite to that of the incident rays, is taken as negative.
4. Distance measured upward from the principal axis is taken as positive distance.
5. Distance measured downward from the principal axis is taken as negative distance.

Let u = distance of the object from P.
      v = distance of the image from P.

In a concave mirror  or a convex mirror, u is always negative, as PA distance is measured in the direction opposite to that of the light rays striking the mirror surface. In a concave mirror, v can sometimes be positive and sometimes be negative. For convex mirrors, v is always positive.

The focus of a concave mirror is considered negative in sign. The focus of the convex mirror, on the other hand is always positive in sign.

Mirror formula
The mirror formula gives the relationship between the object distance u, the image distance v and the focal length f. The formula is written as

      1                   1                       1
      +             =   
      u                   v                        f

Thus if we know two of the three quantities from u,v,f, we will be able to find the third quantity. The values of u,v and f have to be inserted with proper sign convention.

Linear magnification of mirrors
We have seen earlier with different position of the object in front of the spherical mirror surfaces, the image can be either magnified or diminished; the image can be either erect or inverted. The ratio of the height of the image to the height of the object is known as the magnification.

                                  Height of the image
Magnification =   
                                  Height of the object

If we say that
h₁ = Height of the object
h₂ = Height of the image,

                                               h₂
then magnification     m =    
                                               h₁

From the sign convention mentioned earlier,  a positive sign of m indicates that the image is virtual and erect. A negative sign of m indicates that the image is real and inverted.

Magnification is called as the linear magnification, because we are calculating the linear height of the object and images.

Those of you familiar with similar triangles, will immediately understand that

           h₂                        v
m =      =     
           h₁                      u  

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