MHT CET · Physics · Ray Optics

Some water is filled in a container of height 30 cm . If is is to appear half filled to the observer when viewed from the top of the container, the height upto which water should be filled in it, is [Refractive index of water \(=\frac{4}{3}\) ]

A 15 cm
B 18 cm
C 20 cm
D 24 cm

Verified Solution

Answer & Solution

Correct Answer

(C) 20 cm

Step-by-step Solution

Detailed explanation

Refractive index of a medium is given by,
n= Real depth/ Apparent depth...(i)
Given that, height of container \(=30 \mathrm{~cm}\)
Apparent depth \(=15 \mathrm{~cm}\)...(ii)
Real depth \(=\mathrm{n} \times\) Apparent depth \(\ldots[\) From (i) \(]\)
Given that, \(n_w=\frac{4}{3}\)...(iii)
...(iii)
Real depth \(=20 \mathrm{~cm}\)
...[From (ii) and (iii)]
\(\therefore \quad x=20 \mathrm{~cm}\)

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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