Reflection Test - 7

Plane mirror always forms a virtual image of the real object for all the rays emitted by the object. So, when a point source of light is placed in front of a  plane mirror, all the reflected rays met at a point when produced backward.

For getting full image, length of the mirror should be half that of an object(man). 

Length of mirror = 160/2 = 80cm

• The alphabets that do not show lateral inversion when viewed through a plane mirror are I, O, A, V, W, M, H, T, U, V, X, Y.
• The change of sides of an object in its mirror image is called lateral inversion.
• It happens due to the reflection of light.

Important Points

• A reflection appears to be the same distance from the other side of the mirror as the viewer's eyes are from the mirror.
• Refraction is the bending of light rays.
  • Normally, light travels in a straight line and changes direction and speed when it passes from one transparent medium to another.
• The three most common mirror glass types are:

  Plane Mirror	These are flat mirrors that reflect images in their normal proportions, reversed from left to right.
  Concave Mirror	Concave mirrors are spherical mirrors that curve inward like a spoon. They create the illusion of largeness.
  Convex Mirror	Convex mirrors are also spherical mirrors. They bulge out and distort the reflected image, making it smaller.

Additional Information

• The laws of reflection of light apply to both plane mirrors as well as spherical mirrors.
  • The first law of reflection: The incident ray, reflected ray and normal, all lie in the same plane.
  • The second law of reflection: The angle of reflection is always equal to the angle of incidence.

We see from the figure that the observer and the image is 10 + 30 = 40cm

The magnification produced by a plane mirror is +1 implies that the image formed by a plane mirror is virtual, erect and of the same size, as that of object.

Given that,

The distance of object from plane mirror D=100cm

So, initial distance of image and object

= 100 − (−100)

= 200cm

Now, object approaches the mirror with the speedv=5cm/s  

So, distance travelled by object in 6 sec

D = 5 × 6

D = 30 cm

At this instant,

Distance between mirror and object

D = 100 − 30

D = 70cm

Now, the distance between image and object is

D = 70 − (−70)

D = 140cm

In a plane mirror if the mirror moves at speed of v, then the image moves at a speed of 2v.

So, in this case, as mirror is moving at a speed 10 cm/s, the image will move at a speed of (2) × (10) cm/s = 20cm/s

Distance of Image formed in the mirror is same as the distance of the object form the surface of the mirror.

Thus is distance of object = u

Then distance of image = -u (as the image is formed at other side of the mirror)

Thus distance between image and object = 2u...(1)

Now if mirroe is approaching you/object with speed v, then distance travelled by mirror in unit time = v units

Thus distance between mirror and object in unit time = u - v

Thus disatnce between object and its image = 2(u-v)....(2)

From equations (1) and (2) distance between image and object is reduced by 2v units in unit time(1 second)

Thus speed of image w.r.t object = 2v

so in this case The image moves towards the mirror with a speed v

x’ = -x, where x is position of observer and x’ is position of the image.

With mirror at 0.

So, if dx/dt = 2 m/s, dx’/dt = -dx/dt = - 30m/s.

using the classical formula for relative speed,

Vrel = dx’/dt - dx/dt = -2dx/dt = -60m/s.

So, the image is approaching the observer at 60 m/s. 

Let us consider that the object distance from the mirror is u=a

As in the case of a plane mirror, the image distance is equal to the object distance is same, hence

v = a

Therefore the distance between the object and image will be d = 2a