COMEDK · Physics · 25. Ray Optics

A fish in water (refractive index \(n\) ) looks at a bird vertically above in the air. If \(y\) is the height of the bird and \(x\) is the depth of the fish from the surface, then the distance of the bird as estimated by the fish is

A \(x+y\left(1-\frac{1}{n}\right)\)
B \(x+n y\)
C \(x+y\left(1+\frac{1}{n}\right)\)
D \(y+x\left(1-\frac{1}{n}\right)\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(x+n y\)

Step-by-step Solution

Detailed explanation

When object is in rarer medium and observer is in denser medium, then normal shift, \(d=(n-1) h\) where, \(h=\) real depth \(=y\) Now, apparent depth or the apparent height of the bird from the surface of the water \(=y+(n-1) y=n y\). The total distance of the bird as estimated…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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