Question

An arrow object is viewed through a bent metal tube with the help of four plane mirrors A, B, C and D as shown in the figure. Every mirror is inclined at an angle of $45^\circ$ with the horizontal. Which of the following represents correct images made by these mirrors in sequence?

• A. $\uparrow \longrightarrow \longrightarrow \uparrow$
• B. $\longleftarrow \uparrow \longrightarrow \uparrow$
• C. $\longrightarrow \downarrow \longleftarrow \uparrow$
• D. $\uparrow \downarrow \uparrow \downarrow$

Answer 1

Answer: (B)

$\longleftarrow \uparrow \longrightarrow \uparrow$

Answer 2

In the U–shaped tube the four mirrors are arranged with their reflecting faces inclined at 45° with the horizontal. Depending on their relative orientations (i.e. which side of the tube they are on) the “normal” (perpendicular to the mirror surface) points along different directions. Applying the law of reflection (using the rule that the image‐direction is given by ϕ′ = 2ϕ_normal – ϕ_object) one finds that the upward pointing arrow (object) is first “rotated” by mirror A to point leftwards; then mirror B restores it to point upward; mirror C gives an image pointing to the right; and finally mirror D produces an image pointing upward. That is, the successive images (in order A, B, C, D) are

left–arrow, upward–arrow, right–arrow, upward–arrow.