Question

A man is looking down a 9m deep tank filled with a transparent liquid of refractive index √3. The line of sight of the man makes an angle of 30° with the horizontal. What is the depth of the tank as seen by the man?

Answer 1

Hello Dear.

Here is the answer---

Real Depth of the tank = 9 m.
Refractive Index of the liquid(μ) = √3

∵ μ = Real Depth/Apparent Depth
∴ Apparent Depth = Real Depth/μ
∴ Apparent Depth = 9/√3
∴ Apparent Depth = 9/√3 × √3/√3
⇒ A.D. = 3√3 m.
⇒ A.D. = 3 × 1.732
⇒ A.D. = 5.196 m.


Thus, the depth of the tank as seen by the man is 5.196 m.

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Also,angle made by the line of sight with the Horizontal(or angle of Incidence) = 30°

Now, μ =Sin i/Sin r
⇒ √3 = Sin 30°/Sin r
⇒ Sin r = 1/2 ÷ √3
⇒ Sin r = √3/2
⇒ Sin r = Sin 60°

On Comparing,
  r = 60°
Thus, angle of Refraction is 60°.


Hope it helps.