Images formed by flat mirrors

Images formed by flat mirrors

We begin by considering the simplest possible mirror, the flat mirror. Consider a point source of light placed at O in Figure 36.1, a distance p in front of a flat mirror. The distance p is called the object distance. Light rays leave the source and are reflected from the mirror. Upon reflection, the rays continue to diverge (spread apart), but they appear to the viewer to come from a point I behind the mirror. Point I is called the image of the object at O. Regardless of the system under study, we always locate images by extending diverging rays back to a point from which they appear to diverge. Images are located either at the point from which rays of light actually diverge or at the point from which they appear to diverge. Because the rays in Figure 36.1 appear to originate at I, which is a distance q behind the mirror, this is the location of the image. The distance q is called the image distance. Images are classified as real or virtual. A real image is formed when light rays pass through and diverge from the image point; a virtual image is formed when the light rays do not pass through the image point but appear to diverge from that point. The image formed by the mirror in Figure 36.1 is virtual. The image of an object seen in a flat mirror is always virtual. Real images can be displayed on a screen (as at a movie), but virtual images cannot be displayed on a screen.

We can use the simple geometric techniques shown in Figure 36.2 to examine the properties of the images formed by flat mirrors. Even though an infinite number of light rays leave each point on the object, we need to follow only two of them to determine where an image is formed. One of those rays starts at P, follows a horizontal path to the mirror, and reflects back on itself. The second ray follows the oblique path PR and reflects as shown, according to the law of reflection. An observer in front of the mirror would trace the two reflected rays back to the point at which they appear to have originated, which is point P’ behind the mirror. A continuation of this process for points other than P on the object would result in a virtual image (represented by a yellow arrow) behind the mirror. Because triangles PQR and P’QR are congruent, PQ = P’Q. We conclude that the image formed by an object placed in front of a flat mirror is as far behind the mirror as the object is in front of the mirror. Geometry also reveals that the object height h equals the image height h’. Let us define lateral magnification M as follows: This is a general definition of the lateral magnification for any type of mirror. For a flat mirror, M = 1 because h’ = h.
Finally, note that a flat mirror produces an image that has an apparent left–right reversal. You can see this reversal by standing in front of a mirror and raising your right hand, as shown in Figure 36.3. The image you see raises its left hand. Likewise, your hair appears to be parted on the side opposite your real part, and a mole on your right cheek appears to be on your left cheek. This reversal is not actually a left–right reversal. Imagine, for example, lying on your left side on the floor, with your body parallel to the mirror surface. Now your head is on the left and your feet are on the right. If you shake your feet, the image does not shake its head! If you raise your right hand, however, the image again raises its left hand. Thus, the mirror again appears to produce a left–right reversal but in the up–down direction!
The reversal is actually a front–back reversal, caused by the light rays going forward toward the mirror and then reflecting back from it. An interesting exercise is to stand in front of a mirror while holding an overhead transparency in front of you so that you can read the writing on the transparency. You will be able to read the writing on the image of the transparency, also. You may have had a similar experience if you have attached a transparent decal with words on it to the rear window of your car. If the decal can be read from outside the car, you can also read it when looking into your rearview mirror from inside the car.

We conclude that the image that is formed by a flat mirror has the following properties. 

SI UNITS

Motion under gravity

Motion of Body Under Gravity (Free Fall)

The force of attraction of earth on bodies, is called force of gravity. Acceleration produced in the body by the force of gravity, is called acceleration due to gravity. It is represented by the symbol g.

In the absence of air resistance, it is found that all bodies (irrespective of the size, weight or composition) fall with the same acceleration near the surface of the earth. This motion of a body falling towards the earth from a small altitude (h << R) is called free fall.

An ideal example of one-dimensional motion is motion under gravity in which air resistance and the small changes in acceleration with height are neglected.

 (1) If a body is dropped from some height (initial velocity zero)

(i) Equations of motion : Taking initial position as origin and direction of motion (i.e., downward direction) as a positive, here we have

 

     u = 0            [As body starts from rest]

     a = +g       [As acceleration is in the direction of motion]

      v = g t                                    …(i)

                                  …(ii)

                                  …(iii)

                          ...(iv)

(ii) Graph of distance, velocity and acceleration with respect to time :

              

(iii) As h = (1/2)gt², i.e., h µ t², distance covered in time t, 2t, 3t, etc., will be in the ratio of 1² : 2² : 3², i.e., square of integers.

(iv) The distance covered in the nth sec,

So distance covered in 1^st, 2^nd, 3^rd sec, etc., will be in the ratio of 1 : 3 : 5, i.e., odd integers only.

(2) If a body is projected vertically downward with some initial velocity

Equation of motion :     

    

(3) If a body is projected vertically upward

(i) Equation of motion : Taking initial position as origin and direction of motion (i.e., vertically up) as positive

a = – g  [As acceleration is downwards while motion upwards]

So, if the body is projected with velocity u and after time t it reaches up to height h then

;;;

(ii) For maximum height v = 0

So from above equation u = gt,

and     

(iii) Graph of displacement, velocity and acceleration with respect to time (for maximum height) :

 

It is clear that both quantities do not depend upon the mass of the body or we can say that in absence of air resistance, all bodies fall on the surface of the earth with the same rate.

(4) The motion is independent of the mass of the body, as in any equation of motion, mass is not involved. That is why a heavy and light body when released from the same height, reach the ground simultaneously and with same velocity i.e.,  and .

(5) In case of motion under gravity, time taken to go up is equal to the time taken to fall down through the same distance. Time of descent (t₂) = time of ascent (t₁) = u/g

\ Total time of flight T = t₁ + t₂

(6) In case of motion under gravity, the speed with which a body is projected up is equal to the speed with which it comes back to the point of projection.

As well as the magnitude of velocity at any point on the path is same whether the body is moving in upwards or downward direction.

(7) A body is thrown vertically upwards. If air resistance is to be taken into account, then the time of ascent is less than the time of descent.  t₂ > t₁

Let u is the initial velocity of body then time of ascent   and  

where g is acceleration due to gravity and a is retardation by air resistance and for upward motion both will work vertically downward.

For downward motion a and g will work in opposite direction because a always work in direction opposite to motion and g always work vertically downward.

So    

Þ   

Þ                            

Comparing t₁ and t₂ we can say that t₂ > t₁

since (g + a ) > (g – a)