Question

$ {L_1} $ and $ {L_2} $ are two lines. If the reflection of $ {L_1} $ on $ {L_2} $ and the reflection of $ {L_2} $ is on $ {L_1} $ coincides then, the angle between the line is
A. $ {30^0} $
B. $ {60^0} $
C. $ {45^0} $
D. $ {90^0} $

Answer 1

Hint: In this question, we need to determine the angle between the lines $ {L_1} $ and $ {L_2} $ such that their reflection on one another coincides with each other. For this, we will use the properties of reflection which relates the angle of incidence and angle of reflection.

Complete step-by-step answer:

Let the angle between $ {L_1} $ and $ {L_2} $ be ‘x’.

The following sketch depicts the pictorial representation of the lines and their reflection.

According to the question, the reflection of $ {L_1} $ on $ {L_2} $ and the reflection of $ {L_2} $ is on $ {L_1} $ coincides so, from the above shared figure we can say that the reflection of $ {L_1} $ makes an angle of ‘x’ with $ {L_2} $ .

At the same time, the reflection of $ {L_2} $ makes an angle of ‘x’ with $ {L_1} $ .

So, the above figure can also be drawn as:

Following the property of the straight lines, the sum of the angles on a straight line is 180 degrees.

From the above figure, the Reflection line is a straight line on which three equal angles (angle between the lines, reflection of the first line on the second line and the reflection of the second line on the first line) are present whose magnitude is ‘x’ each.

So, $ x + x + x = 180 $

Solving the above equation for the value of ‘x’.

 $

\Rightarrow 3x = 180 \\

  x = \dfrac{{180}}{3} \\

   = 60 \\

  $

Hence, the angle between the lines $ {L_1} $ and $ {L_2} $ is 60 degrees.

So, the correct answer is “Option B”.

Note: It is interesting to note here that the reflection of both the lines on each other will always be equal if the angle between them remains constant at 60 degrees. In other words, if the lines are at 60 degrees then, we can see only one reflection as they coincide with each other.