Question

In a pond of water, a flame is held 2 m above the surface of water. A fish is at depth of 4 m from water surface. Refractive index of water is $\frac{4}{3}$. The apparent height of the flame from the eyes of fish is:

• (A) $5.5$ m
• (B) $6$ m
• (C) $\frac{8}{3}$m
• (D) $\frac{20}{3}$m
  Correct Answer

Answer 1

The Correct Option is D

Explanation:
Given:Depth of the fish from the surface of the water = 4 mHeight of the flame BC = 2 mRefractive index of the water, $\mu =\frac{4}{3}$We have to find the the apparent height of the flame from the eyes of the fish. The ray diagram is shown below:

When viewed from the rarer medium, the apparent height isApparent height$=\frac{\text{Real height}}{\text{Refractive index of the denser medium}}$But, when viewed from the denser medium, the apparent height isApparent height$=$Real height $\times$ Refractive index of the deser medium$\Rightarrow AC=BC\times \mu$$\Rightarrow AC=2\times \frac{4}{3}=\frac{8}{3}$$\Rightarrow AC=\frac{8}{3}$Thus, the total apparent height of the flame from the eyes of the fish is$AD=AC+CD$$\Rightarrow AD=\frac{8}{3}+4m=\frac{20}{3}m$Hence, the correct option is (D).

Answer 2

Real Depth and Apparent Depth

Real Depth is the real distance of an object under the surface as determined by immersing it with an accurate ruler.

The depth of an item in a denser media, as perceived from a rarer medium, is referred to as apparent depth in a medium. Its value is less than the real depth.

The relationship between the real depth and the apparent depth is given by

Real depthApparent depth=21=21

Where

• 𝜇₂ = refractive index of the denser medium
• 𝜇₂ = refractive index of the rarer medium
• 𝜇¹₂ = refractive index of the denser medium with respect to the rarer medium

If an object lying in denser medium and is observed from rarer medium, then

Real depthApparent depth=21>1

⇒ Real depth > Apparent depth

That is why, the river bed appeared shallow

If an object lying in rarer medium and is observed from denser medium, then

Real depthApparent depth=21<1

⇒ Real depth < Apparent depth

That is why high flying airplanes appear to be higher than its actual height.