Physics - Geometrical Optics Question with Solution | TestHub
A fluorescent lamp of length 1 m is placed horizontally at a depth of 1.2 m below a ceiling. A plane mirror of length 0.6 m is placed below the lamp parallel to and symmetric to the lamp at a distance 2.4 m from it as shown in figure. Find the length (distance between the extreme points of the visible region along x-axis) of the reflected patch of light on the ceiling.
Answer:
Solution:
Use the image method: reflect the ceiling in the plane of the mirror.
The lamp is 1.2 m below the ceiling and the mirror is 2.4 m below the lamp, so the image of the ceiling lies 3.6 m below the mirror.
Extreme ray: from the lamp end (x = -0.5 m) through the mirror edge (x = 0.3 m): vertical drop 2.4 m over 0.8 m horizontal, slope = 3.
Extending this line 3.6 m further down to the image ceiling: Δx = 3.6/3 = 1.2 m, so the ray meets the ceiling at x = 0.3 + 1.2 = 1.5 m.
By symmetry the reflected patch extends from -1.5 m to +1.5 m, so its length is 3.00 m.
