1. Given Data

• Depth of bulb (h): 80 cm = 0.8 m
• Refractive Index of water (n): 1.33

2. Concept

Light from the source can emerge out of the water surface only if the angle of incidence is less than the Critical Angle (C). Rays hitting the surface at an angle greater than C undergo total internal reflection.

This creates a circular patch of light on the surface. To find the area, we first need to calculate the radius (R) of this circle.

3. Calculation

Step A: Formula for Radius

From the geometry of the critical angle, the radius (R) is given by:

R = h / √(n² - 1)

Step B: Substituting Values

First, calculate the denominator:

• n² = (1.33)² = 1.7689
• n² - 1 = 0.7689
• √(0.7689) ≈ 0.877

Now, calculate the radius (R):

• R = 0.8 / 0.877
• R ≈ 0.912 m

Step C: Area Calculation

The area of the surface is a circle:

Area = π × R²

Area = 3.14 × (0.912)²

Area = 3.14 × 0.8317

Area ≈ 2.61 m²

Conclusion: The light from the bulb emerges through a circular area of approximately 2.61 square meters on the water surface.