A transparent solid slab of refractive index 1.5 rests on a pool of transparent liquid of refractive index 2.0 . A small air bubble is trapped inside the solid slab. When viewed normally from the air above the slab, the apparent depth of the bubble is 4 cm . When viewed normally from the liquid below the slab, the apparent depth of the bubble is 6 cm . The actual total thickness of the solid slab is:

Step-by-step solution

Let the actual distance of the bubble from the top surface of the slab be x₁ and from the bottom surface be x₂ . The formula for apparent depth is given by: h_ app = h_ actual n_ observer n_ object When viewed from the top (observer in air, n_ air = 1 ): 4 = x₁ 1 1.5 x₁ = 4 1.5 = 6 cm When viewed from the bottom (observer in liquid, n_ liquid = 2.0 ): 6 = x₂ 2.0 1.5 x₂ = 6 1.5 2.0 = 4.5 cm The total actual thickness of the solid slab is the sum of these two distances: Thickness = x₁ + x₂ = 6 + 4.5 = 10.5 cm Answer: