A vessel, whose bottom is flat and perfectly reflecting, is filled with water (index = 4/3) upto a height = 40 cm. A point object in air above is moving towards the water surface with a constant speed = 4m/s. What is the relative speed of its final image (in m/s), as seen by the object itself, at a moment when the object is 30cm above the water surface?
Physics · Mixed Chapter
JEE Mains

Question

A vessel, whose bottom is flat and perfectly reflecting, is filled with water (index = 4/3) upto a height = 40 cm. A point object in air above is moving towards the water surface with a constant speed = 4m/s. What is the relative speed of its final image (in m/s), as seen by the object itself, at a moment when the object is 30cm above the water surface?

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Consider the point object a distance h above water. Viewed through a flat water surface from air, a plane reflecting surface at real depth d=40 cm appears at depth d/μ=40/(4/3)=30 cm. Step 2: After reflection at the immersed bottom and refraction back to air, the final virtual image is at a depth h+2d/μ below the surface (paraxial approximation). Step 3: As the object moves down at speed 4 m/s, h decreases at rate dh/dt=−4 m/s. The image depth h+2d/μ also decreases at 4 m/s, i.e. image…