Question

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is \( 4/3 \) and the fish is 12 cm below the surface, the radius of this circle (in cm) is

• A. \( 3 \sqrt{5} \)
• B. \( 4 \)
• C. \( 6 \sqrt{7} \)
• D. \( 36/\sqrt{7} \)

Hint:

To find the radius of the circular horizon seen by a fish under water, use Snell’s Law and the refractive index of the water.

Answer 1

The Correct Option is A

Step 1: Using Snell's Law.
From Snell's Law and the geometry of the situation, the radius \( r \) of the circle is related to the depth \( h \) of the fish by the equation: \[ r = h \cdot \sqrt{\frac{n^2 - 1}{n^2}} \] where \( n \) is the refractive index of water and \( h = 12 \, \text{cm} \). Substituting \( n = 4/3 \) gives: \[ r = 3 \sqrt{5}. \] Step 2: Conclusion.
The correct answer is (A), \( 3 \sqrt{5} \).