Answer to Question #141755 in Optics for Bernita

Question

A boy 115cm in height is standing at a distance of 65cm from a vertical mirror 50cm in length, the upper edge of which is 125cm from the floor. Talking the boy's eye level to be 98cm above the floor, determine with the help of a diagram

a) how much of his height will be seen by him in the mirror

b) what length of the mirror is useful to him

Answer 1

a) The top of boy’s head is at point A, his eyes are at point B, and the floor is at point E. Lines AD and CF are perpendicular. The line CF is a normal to the mirror surface. Since the angle of incidence is equal to the angle of reflection, the triangles BCF and DCF are congruent and CD = BC.

The bottom of the mirror (point F) is at 75 cm above the floor (125-50). Boy’s eyes (point B) are 23 cm above the bottom of the mirror (98-75). The mirror is tall enough that he will be able to see to the top of his head (point A).

Boy’s height will be seen by him in the mirror = AB + BC + CD = 23 + 23 +17 = 63 cm.

b) The boy will use all the mirror length from the bottom of the mirror (point F) up to the level of his eyes (point O) which is 23 cm (98-75). The top of his head (point A) is 17 cm above the level of his eyes (115-98). Since the mirror is only half way to his image divide this by 2, i.e. 8.5 cm. Thus, the length of the mirror is useful to boy = OF + HO = 23 + 8.5 = 31.5 cm