Question

In the given figure, a mirror is arranged at an angle ${30}^{\circ }$ to the square shaped wooden board as shown. Find the angle made by the comb with its reflected shadow. [5 MARKS]

Answer 1

Diagram: 2 Marks
Explanation: 3 Marks

Given that the mirror makes ${30}^{\circ }$ with board.

i.e., BAP= ${30}^{\circ }$

In triangle ABP, as APB= ${90}^{\circ }$and as sum of angles in a triangle is ${180}^{\circ }$,

PBA = ${60}^{\circ }$

DP and EO are parallel lines and AB is transversal.

So, PBA = BOE = ${60}^{\circ }$

As OX is normal to mirror AB, BOX= BOE + EOX= ${90}^{\circ }$

That implies the angle of incidence, EOX= ${30}^{\circ }$

According to the law of reflection, Angle of incidence = Angle of reflection

i.e., EOX= XOC= ${30}^{\circ }$

In right triangle EOC, EOC= EOX + XOC=${60}^{\circ }$

In triangle EOC, as OEC= ${90}^{\circ }$and as sum of angles in a triangle is ${180}^{\circ }$,

OCE=${30}^{\circ }$ which is the required angle.