The image of an object placed at a point A before a plane mirror LM is seen at the point B by an observer at D as shown in Fig. 7.12. Prove that the image is as far behind the mirror as the object is in front of the mirror.[Hint: CN is normal to the mirror. Also, angle of incidence = angle of reflection]

Solution:

Given, LM is a plane mirror.

The image of an object placed at a point A before the mirror LM is seen at point B by an observer at D.

We have to prove that the image is as far as behind the mirror as the object is in front of the mirror.

Angle of A = ∠1 = 90°

Angle of B = ∠2 = 90°

Considering triangles OBC and OAC,

Common side = OC

∠1 = ∠2

We know that the angle of incidence is equal to the angle of reflection.

∠i = ∠r

Multiplying by -1 on both sides,

(-1)∠i = (-1)∠r

-∠i = -∠r

Multiplying by 90° on both sides,

90° - ∠i = 90° - ∠r

From the figure,

∠ACO = 90° - ∠i

∠BCO = 90° - ∠r

So, ∠ACO = ∠BCO

ASA criterion states that two triangles are congruent, if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle.

By ASA criterion, the triangles OAC and OBC are congruent.

By CPCT,

OA = OB

Therefore, the image is as far as behind the mirror as the object is in front of the mirror.

✦ Try This: In ΔPQR. ∠R = ∠P and QR = 4 cm and PR = 5 cm, then length of PQ is:

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 7

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NCERT Exemplar Class 9 Maths Exercise 7.4 Problem 2

The image of an object placed at a point A before a plane mirror LM is seen at the point B by an observer at D as shown in Fig. 7.12. Prove that the image is as far behind the mirror as the object is in front of the mirror.[Hint: CN is normal to the mirror. Also, angle of incidence = angle of reflection]

Summary:

The image of an object placed at a point A before a plane mirror LM is seen at the point B by an observer at D as shown in Fig. 7.12. It is proven that the image is as far behind the mirror as the object is in front of the mirror by CPCT

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