In a simple periscope, two identical plane mirrors are fixed parallel to each other, each inclined at 45∘ to the vertical. A distant horizontal beam of light is incident on the top mirror.
(a) Show that the beam emerges from the lower mirror travelling horizontally.
(b) If the top mirror is accidentally rotated so that it now makes an angle of 50∘ with the vertical (keeping the lower mirror unchanged at 45∘ to the vertical), calculate:
(i) the new angle of incidence on the top mirror,
(ii) the direction of the reflected beam leaving the top mirror (express as angle to the vertical),
(iii) the angle of incidence on the lower mirror,
(iv) the final direction of the beam emerging from the lower mirror.