Light - Part III

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

A ray of light AB is incident on the concave mirror MMí. AB is parallel to the principal axis XP. On reflection at point B, the path of the ray of light changes. The ray of light now becomes BFY and passes through F.  

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

This follows from simple geometrical consideration. A line from C to MMí is actually the radius of the sphere. The radius is always perpendicular at the point of contact on the spherical surface. A ray traveling along the normal to the mirror, always gets reflected along back along the normal itself.  

Third Rule :  The third rule is inverse of the first rule. When a ray of light passes through the focus F and strikes the mirror MMí, the reflected ray is parallel to the principal axis XP.  

A ray of light AE is striking the mirrored surface at an angle. AE is passing through the focal point F. On reflection at point E, the ray of light takes the path EG. Line EG is parallel to the principal axis XP.

From the above three rules, now we can study how images are formed with the help of concave mirrors. The type of images formed depends on where the object is positioned in front of the mirror. We will study a few typical cases.
Case 1 : object is placed between the pole P and the focus F
Case 2 : object is placed at focus F
Case 3 : object is placed between the focus F and the centre of curvature C.
Case 4 : object is placed at the centre of curvature C.
Case 5 : object is placed at a distance beyond C.
Case 6 : object is placed at a far off distance beyond C (or at infinite distance).

Case 1 : Image formed by a concave mirror when the object is placed between the pole P and the focus F.

Consider the following figure.

Let the object be a candle AB placed between F and P.

Consider two rays of light starting from A. A light ray from A, parallel to CP will strike MMí at D. This ray of light, on reflection will pass through F (rule 1). The second light ray from A passing through CA, will go un-deviated and will get reflected back along AC (rule 2).

The other end of the candle B. is placed along the principal axis CP. So any ray of light BP will get reflected back along PB itself (rule 2).

Now extend all the reflected rays, in front of MMí and behind MMí. You will notice that the rays emanating from A are intersecting at a point Aí behind MMí. Rays of light from B extending behind the mirror MMí, forms an image Bí. The reflected image is AíBí behind the mirror. You can see that the size of AíBí is larger than AB.

Thus we can conclude that for an image of an object placed between F and P of a concave mirror :

• The image is behind the mirror and hence is virtual

• The image is erect and not inverted

• The image is magnified

This shows why concave mirrors are used as shaving mirrors. If you place your face close to the mirror, the image will be large and erect. If you place your face at any other position, the image is seen to be blurred or defocused. Such a situation is not seen in case of a plane mirror.  

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