Plane Mirrors. 

          All mirrors have a silvery surface at the back of the glass sheet. (This is normally covered by another coat of protective material). They produce images due to regular reflection of light.

"Mirror mirror, Who is the prettiest of all?"

 I see my image on the mirror, but where exactly is the image?

Laws of reflection.

1.      When a ray of light gets reflected the angle of incidence become equal to the angle of reflection.

2.      The incident ray, the reflected ray and the Normal remain in the same plane.

Example:-

The illustration shows a red ray getting reflected by the mirror. 

The green line shows the path of the ray falling on the mirror while the red line depicts the path it will take after reflection.

The angle marked as “ i “,  is known as the angle of incidence and the other , angle “r” as the angle of reflection. 

So by the first law ………  ∠ i.  =  ∠ r. 

If "i" 38 ˚ ∠ "r" also has to be 38 ˚.

Fig.1. A mirror or Looking Glass.

Normal is the straight line that will be perpendicular to the mirror from all sides.

According to the 2^nd Law, the two rays and the normal would be in the same plane.

Ray diagrams

We can get the properties of the images formed by mirrors by drawing ray diagrams.

Fig.3 Formation of an image by a plane mirror.

Two rays reaching the mirror from the candle are shown in red. One that is perpendicular to the mirror comes back along the same path. 

The other gets reflected making angle I = angle r. 

We can get the position of the image by producing the lines as shown by dotted lines. The lines only show the red tip of the candle flame. By drawing lines from blue base of the flame it is possible to get the position of that too.

All about the image of a plane mirror.

1.      The image is virtual.  2.      The size of image is equal to the size of the object. 3.      The image is not identical to the object but laterally inverted.  4.      The image is formed behind the mirror. 5.      The image distance is equal to the object distance.

a.      It cannot be obtained on a screen and therefore it is not real. a.      The right side goes to the left and left side to right. (Laterally inverted)   d i    =  d o.

Find out.

1.      If the surface of a plane mirror turns by an angle of 20 ˚ what will be change of the angle made by a reflected ray?

2.      If two plane mirrors are placed at an angle of 90 ˚. How many images can you get of an object placed in the angle?

3.      What is a kaleidoscope? Try to make one.

4.   What is a periscope?

 

Curved mirrors.

There are many types of curved mirrors but the two most important in our study are the spherical mirrors known as convex and concave mirrors.

Fig. 4. Convex mirror reflects a parallel beam as diverging rays.

If you complete the circle of the mirror segment, the centre of that is called the Centre of curvature.

Any line drawn from the Centre of curvature, passing the mirror will be a normal to the mirror surface.

The horizontal line drawn from ‘C’, passing through the centre of the mirror is the principal axis.

All rays parallel to the principal axis will get reflected as coming from one point which is half way between ‘P’ and ‘C’.  This point is the Principal Focus.

PC is the radius of curvature.

Fig.5. A concave mirror converges a parallel beam to the Focus.

Images by Convex mirrors.

      The properties of images formed may be obtained by drawing ray diagrams. 

Just two rays are sufficient to get the image position of an object. The two rays we consider are

i.      A ray parallel to the main axis coming from the top of the object.This will get reflected as if coming from the focus.

II.     A ray going towards the centre of curvature will return along the same path.

Fig.6 An image formed by a convex mirror.

The Properties of the Image.

1. The image is formed behind the mirror.
2. It is virtual.
3. It is upright and much smaller than the object.
4. The image distance is smaller than the object distance. ( The distances are measured from P.)
   

      The position of the image and the size can also be determined by a calculation.

Calculating the position of the image.

For mirror calculations the image distance d_i, the object distance d_o and the focal length are measured from the pole ‘P’ of the mirror. For real images and real rays the values are taken as positive and for virtual distances are taken as negative.

In the above diagram PO = d_o = 12 cm.  (We have taken measurements to the nearest cm to make it easier)

The Radius PC = 6. cm.  Therefore PF =f =  6/2  = -  3 cm.

Remember focal length is half the radius. That is f = 1/R.

The Mirror Formula

 1/d_i + 1/d_o = 1/f

Using them in the formula to find the image distance we get:-

1/d_i = - 1/12 - 1/3

1/d_i = -1 -4 / 12

   d_i = - 2.4 cm.

 Images by Concave mirrors.

Just the way we have done, try to draw ray diagrams and find out the nature of images formed as the object distance varies.