Question

A beaker is filled with water (refractive index \( \frac{4}{3} \)) up to a height \( H \). A coin is placed at its bottom. The depth of the coin, when viewed along the near normal direction, will be:

• A. \( 3H \)
• B. \( \frac{3H}{4} \)
• C. \( H \)
• D. \( \frac{4H}{3} \)

Hint:

The apparent depth of an object in a transparent medium is given by dividing the real depth by the refractive index of the medium.

Answer 1

The Correct Option is B

The apparent depth of an object seen through a medium is given by: \[ d_{\text{apparent}} = \frac{d_{\text{real}}}{n} \] where \( n \) is the refractive index of the medium, and \( d_{\text{real}} \) is the real depth. Given that the refractive index of water is \( n = \frac{4}{3} \), the apparent depth of the coin will be: \[ d_{\text{apparent}} = \frac{H}{\frac{4}{3}} = \frac{3H}{4} \] Thus, the correct answer is \( \frac{3H}{4} \).