A large square container with thin transparent vertical walls and filled with water (refractive index 34) is kept on a horizontal table. A student holds a thin straight wire vertically inside the water 12 cm from one of its corners, as shown schematically in the figure. Looking at the wire from this corner, another student sees two images of the wire, located symmetrically on each side of the line of sight as shown. The separation (in cm) between these images is ____.
Solution
The question involves refraction at the water-air interface viewed from the corner of the container. Using Snell's law at the interface with α=45° and refractive index μ=34:
34sinα=sinθ
This gives sinθ=322.
Applying geometry and refraction relations: AB=cosα12dα=cosθxdθ
From the differentiated form of Snell's law and geometry, we find x=2 cm.
The separation between images is: d=2xsin(θ−α)=4×21(322−31)=38−22≈1.73 cm
Rounding to nearest integer gives approximately 2 cm.
