Question

(a) A water pond appears to be 2.7 m deep. If the refractive index of water is 4/3, find the actual depth of the pond.

(b) A coin is placed at the bottom of a beaker containing water (refractive index = 4/3) to a depth of 12 cm. By what height the coin appears to be raised when seen from vertically above?

(c) A postage stamp kept below a rectangular glass block or refractive index 1.5 when viewed from vertically above it, appears to be raised by 7.0 mm. Calculate the thickness of the glass block.

Answer 1

(a) Given,
Apparent depth = 2.7 m
Refractive index of water μ_w = 4 / 3
Real depth = Apparent depth × μ_w
Real depth = 2.7 × 4 / 3
Real depth = 3.6 m

(b) Given,
Refractive index of the water, μ_w = 4 / 3
Real depth at which coin is placed = 12 cm
Shift in the image = ?
Shift = Real depth × (1 – 1 / μ)
Shift = 12 × (1 – 3 / 4)
Shift = 12 / 4
Shift = 3 cm or R = 3 cm

(c) Given,
Refractive index of the glass block, μ_g = 1.5
Shift in the image = 7 mm or 0.7 cm
Thickness of glass block or real depth = ?
Shift = Real depth × (1 – 1 / μ)
0.7 = R × (1 – 1 / 1.5)
R = (0.7 × 1.5) / 0.5
R = 2.1 cm