Physics question?

(a) You need to draw out a ray-diagram first. Consider a ray from the shoe tip, travels along the floor and incident onto the bottom of the inclined mirror. After reflection on the mirror, the ray then enters the eyes of A.

Hence, the incident ray, the reflected ray and the vertical line represents the height of A (i.e. the line joining the eyes of A to her feet) form a right angle triangle.

Suppose the incident angle is i, the reflected angle is r, we have i = r by the Laws of Reflection. The.angle between the incident and reflected rays is thus i+r = 2i. Therefore, from geometry, it is not difficult to show that i = 20 degrees.

Hence, using that right-angle triangle formed by the rays, we have,
tan(2i) = 1.4/x where x is the distance of A from the bottom of the mirror.
i.e. tan(40) = 1.4/x
x = 1.668 m

(b) The distance of the image of the shoes tip behind the mirror equals to the distance of the shoes tip in front of the mirror.

Hence, distance between the shoes tip and its image = 2 x 1.668 m = 3.336 m

By joining the image and the eyes of A by a straight line, we would obtain a new right-angle triangle. Using Pythagoras' Theorem,

Distance of eyes from image of shoes tip
= square-root(1.4^2 + 3.336^2) m
= 3.618 m

(c) Let the new incident angle be i'. Using a similar right-angle triangle as that in part (a), we have,
tan(2i') = 1.4/0.45
i.e. i' = 36.09 degrees

Since incident angle = reflected angle, by the Laws of Reflection, the reflected rays is rotated by an amount of (2i' - 2i) = 2(i' - i).

Because the reflected ray rotates twice the angle at which the mirror rotates, the mirror thus rotates through an angle of (i' - i), which is equal to (36.09 - 20) degrees = 16.09 degrees.

Therefore, the new inclined angle of the mirror
= (70 - 16.09) degrees
= 53.91 degrees

(Note: you could also find the new inclined angle of the mirror using geometry, after knowing the new incident angle i').