Question

A ray of light falls on a plane mirror A kept at an angle 90° to mirror B as shown in the figure. The angle N is
(1) 30°

(2) 45°

(3) 60°

(4) 90°

Please give step by step explanation.​

Answer 1

Hope it is understandable

Answer 2

REFLECTION

It is given that, two plane mirrors are placed in a way, such that it forms a right angle, where mirror A is the opposite side, mirror B is the adjacent side and is right-angled at O. A ray of light falls on mirror A, gets reflected to the surface of mirror B and again gets reflected somewhere.

If you look at the diagram provided, you will notice that X and Y on the mirrors A and B denotes 'normal', respectively. And the angle of incidence formed in mirror A is 30°.

We will use the laws of reflection and the angle sum property of a triangle to find the answer. Let's start solving!

Laws of reflection:

• The incident ray, the reflected ray and the normal ray at the point of incidence, lie in the same plane.
• The angle of incidence is equal to the angle of reflection.

Since the normal line makes a division into two equal halves (each of 90°), we can say that ∠I = ∠R, also,

$\sf{ \angle I+ \angle G = 90 \degree}$

$\rightarrow \quad{ \sf{30 \degree + \angle G= 90 \degree}}$

$\rightarrow \quad{ \sf{\angle G = 90 \degree - 30 \degree}}$

$\rightarrow \quad{ \sf{\angle G = 60 \degree}}$

Similarly, ∠G = ∠H = 60°, since the angle of incidence is equal to the angle reflection and they make 30° on each side.

We know that XOY is a right angled triangle, where, ∠OXY (H) = 60° and ∠O = 90°.

Angle sum property of a triangle:

• The sum of all the interior angles of a triangle equals to 180°.

By applying this property,

$\sf{\angle OXY + \angle O + \angle OYX = 180 \degree}$

$\rightarrow \quad\sf{60 \degree + 90 \degree + \angle OYX = 180 \degree}$

$\rightarrow \quad\sf{150 \degree + \angle OYX = 180 \degree}$

$\rightarrow \quad\sf{\angle OYX = 180 \degree - 150 \degree}$

$\rightarrow \quad\sf{\angle OYX = 30 \degree}$

Similarly, ∠OYX = ∠Q = 30°. So, as per the laws of reflection, ∠M = ∠N and ∠M = 90° – ∠OYX.

$\rightarrow \quad\sf{ \angle M = \angle N = 90 \degree - 30 \degree}$

$\rightarrow \quad\sf{ \angle M = \angle N =60 \degree}$

$\rightarrow \quad \underline{ \boxed{\sf \red{\angle N = \frak{60 \degree}}}}$

Therefore, the required answer will be 60°. Option (3) is appropriate.