In Fig. 6.15, m and n are two plane mirrors perpendicular to each other. Show that incident ray CA is parallel to reflected ray BD
Solution:
Given, m and n are two mirrors perpendicular to each other.
CA is the incident ray
BD is the reflected ray
We have to show that the incident ray is parallel to the reflected ray.
Draw OA and OB perpendicular to m and n such that
∠BAC = ∠1 + ∠2
Also, ∠1 = ∠2
∠BAC = 2(∠1) or 2(∠2) ---------------- (1)
Similarly, ∠ABD = ∠3 + ∠4
∠3 = ∠4
∠ABD = 2(∠3) or 2(∠4) ---------------- (2)
From the figure,
We observe that m ⊥ n, OA ⊥ m and OB ⊥ n
We know that lines perpendicular to two perpendicular lines are also perpendicular.
So, ∠AOB = 90°
Considering triangle AOB,
∠ABO + ∠BAO + ∠AOB = 180°
90° + ∠2 + ∠3 = 180°
∠2 + ∠3 = 180° - 90°
∠2 + ∠3 = 90°
Multiplying by 2 on both sides,
2(∠2) + 2(∠3) = 2(90°)
2(∠2) + 2(∠3) = 180°
From (1) and (2),
∠BAC + ∠ABD = 180°
We know that a pair of consecutive interior angles are supplementary.
So, angle of incidence is equal to the angle of reflection.
Therefore, CA is parallel to BD.
✦ Try This: In Fig., if 1∥m,n∥p and ∠1=85°, find ∠2.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6
NCERT Exemplar Class 9 Maths Exercise 6.4 Sample Problem 1
In Fig. 6.15, m and n are two plane mirrors perpendicular to each other. Show that incident ray CA is parallel to reflected ray BD
Summary:
The angle of incidence is the angle between this normal and the incident ray; the angle of reflection is the angle between this normal and the reflected ray.In Fig. 6.15, m and n are two plane mirrors perpendicular to each other. It is shown that incident ray CA is parallel to reflected ray BD by the law of reflection which states that the angle of incidence equals the angle of reflection
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