I tried to prove that distance of image is same as the distance of object in a plane mirror.
The image attached is the ray diagram.
First of all, I have assumed object and image to be parallel to mirror.
First I proved angle TSA = angle TSa
Then I have made similar triangle TSA and triangle TSa with AA similarity. ( where angle ATS = angle aTS ----each 90)
Therefore, TS/TS = TA/Ta
=> TA=Ta ( TS/TS = 1 )
=> AS=aS
( corresponding parts of similar triangle are equal in ratio)
Using this, I have made triangle ABS and abs congruent.
where,
As=aS
angle ASB = angle aSB
angle ABS = angle aBS
=> AB=aB ( corresponding parts of congruent triangles are equal)
Therefor, size of image is same as that of object.
Also, Bs=bS
(corresponding parts of congruent triangles)
That is, distance of image from mirror is same as that of object from mirror.
Now, I want to know how to prove that angle of image is same as that of object with principal axis? Because in my above method I already assumed both to be 90 degree. In other words, how to prove that image is erect too?