Question

A rectangular tank of depth 4 m is full of water of refractive index \(\frac{4}{3}\). When viewed from the top, the bottom of the tank is seen at a depth of 

• A. 3 m
• B. 2 m
• C. 0.38 m
• D. 1.33 m

Answer 1

The Correct Option is A

Step 1: Recall the formula for apparent depth.

The apparent depth (\( d_{\text{apparent}} \)) is related to the real depth (\( d_{\text{real}} \)) and the refractive index (\( n \)) of the medium by the formula:

\[ d_{\text{apparent}} = \frac{d_{\text{real}}}{n}. \]

Step 2: Substitute the given values.

The real depth of the tank is \( d_{\text{real}} = 4 \, \text{m} \), and the refractive index of water is \( n = \frac{4}{3} \). Substituting these values:

\[ d_{\text{apparent}} = \frac{4}{\frac{4}{3}} = 4 \cdot \frac{3}{4} = 3 \, \text{m}. \]

Final Answer: The bottom of the tank appears to be at a depth of \( \mathbf{3 \, \text{m}} \), which corresponds to option \( \mathbf{(1)} \).