Question

Prove object distance=image distance for reflection in a plane mirror.​

Answer 1

Answer:

It's proved ~

Explanation:

From the second law of reflection, we have:  

Angle of incidence = Angle of reflection  

So, NAO =  NAX ------ (1)  

Now, OI and NA are parallel lines and OA cuts these parallel lines.

Therefore, the angles MIA and NAX are corresponding angles and hence they are equal. So,  

MIA = NAX ----- (2)  

By comparing equations (1) and (2), we get :  

NAO = MIA ----- (3)  

Now, the angles MOA and NAO are alternate angles and hence equal.  

So, MOA = NAO ------ (4)  

Comparing equations (3) and (4), we get :  

MIA = MOA ----- (5)  

Now, in the triangles MIA and MOA, we have :  

MIA = MOA (just proved)  

IMA = OMA (both are right angles)  

And side MA is common to both the triangles (see Figure above)  

It is clear that the triangles MIA and MOA are congruent triangles and, therefore, their corresponding sides should be equal. Thus :  

IM = OM  

Now, IM represents the distance of image from the mirror and OM represents the distance of object from the mirror. So, we can now say that:  

Distance of image from mirror = Distance of object from mirror

[ took from other site ! but Hope it help , cause you need to know how the answer came NOT from where it came  ]