A container has a liquid of refractive index 1.2 up to height 60 cm. A second immiscible liquid of refractive index 1.6 is added above it to height H. When viewed normally from above, the apparent upward shift of the bottom is 40 cm. Find H in cm.
Physics · Geometrical optics · apperant depth and shift due to slab
JEE Mains 2025 7 April Morning Shift

Question

A container has a liquid of refractive index 1.2 up to height 60 cm. A second immiscible liquid of refractive index 1.6 is added above it to height H. When viewed normally from above, the apparent upward shift of the bottom is 40 cm. Find H in cm.

Physics · Geometrical optics · apperant depth and shift due to slab

JEE Mains 2025 7 April Morning Shift

G1 Physics · Accepted Answer

For normal viewing through plane layers, the apparent depth measured from the top is the sum of each layer thickness divided by its refractive index. Thus, y = H/1.6 + 60/1.2. The real depth is H+60. Given apparent shift = 40 cm: (H+60) - y = 40. Substitute: H+60 - H/1.6 - 60/1.2 = 40. Since 60/1.2 = 50: H - H/1.6 + 10 = 40. H(1-0.625) = 30 ⇒ 0.375H = 30 ⇒ H = 80 cm. Answer: 80.