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GUJCET · Physics · Ray Optics and Optical Instruments
A tank is filled with water to a height of 16 cm . Find the apparent depth of a needle lying at the bottom of the tank is measured by a microscope. Refractive index of water \(\left(\mu_{w}\right)\) is \(\frac{4}{3}\)
- A 8.0 cm
- B 10.6 cm
- C 12.0 cm
- D 9.4 cm
Answer & Solution
Correct Answer
(C) 12.0 cm
Step-by-step Solution
Detailed explanation
(C) 12.0 cm
\(\quad \frac{n \text { (denser) }}{n \text { (rearer) }}=\frac{\text { real depth }\left(h_{2}\right)}{\text { apparent depth }\left(h_{1}\right)}\)
\(
\begin{aligned}
& \therefore & \frac{4}{3} & =\frac{16}{h_{1}} \\
& \therefore & h_{1} & =\frac{16 \times 3}{4} \\
& & & =12 \mathrm{~cm}
\end{aligned}
\)
\(\quad \frac{n \text { (denser) }}{n \text { (rearer) }}=\frac{\text { real depth }\left(h_{2}\right)}{\text { apparent depth }\left(h_{1}\right)}\)
\(
\begin{aligned}
& \therefore & \frac{4}{3} & =\frac{16}{h_{1}} \\
& \therefore & h_{1} & =\frac{16 \times 3}{4} \\
& & & =12 \mathrm{~cm}
\end{aligned}
\)
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