Plane Mirrors — Question 3

Question 3

The image method locates the exact point of reflection

A vertical mirror is the line x=0. An object is at (-2,1) m and an eye is at (-3,4) m in the reflecting half-plane. The mirror is large enough to intercept the needed ray.

1. Find the point where the ray from object to eye strikes the mirror.

2. Find the total reflected path length by replacing the path with a straight segment to the virtual image.

Question 3 - Solution

The image method locates the exact point of reflection

(a) Method and calculation

$$O^\prime=(2,1),\quad E+\lambda(O^\prime-E)=(-3+5\lambda,4-3\lambda).$$$$x=0\Rightarrow\lambda=3/5\Rightarrow\boxed{M=(0,2.2)\,\mathrm m}.$$

(b) Interpretation and further calculation

$$L=|OM|+|ME|=|O^\prime E|.$$$$\boxed{L=\sqrt{5^2+(-3)^2}=\sqrt{34}=5.83095\,\mathrm m}.$$

Physical check

The unfolded straight path has the same length as the reflected path and automatically satisfies equal incidence and reflection angles.