A salt water lake has refractive index 1.4. A fish when looks towards the surface of water, can only view things outside through a circular area. Calculate the semi-vertical angle of the cone formed within which the circular area lies.

Explanation

To solve the problem of finding the semi-vertical angle of the cone formed by the circular area that a fish can see when looking out of a saltwater lake with a refractive index of 1.4, we can follow these steps:

### Step 1: Understand the Problem
The fish is looking out of the water, and we need to determine the angle at which it can see outside the water. This angle will form a cone, and we need to find the semi-vertical angle of that cone.

### Step 2: Apply Snell's Law
When light travels from one medium to another, Snell's law relates the angles of incidence and refraction to the indices of refraction of the two media. The formula is given by:
\[ \mu_1 \sin i = \mu_2 \sin r \]
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