Introduction:
The scenario involves a spider and a fly on the surface of a glass sphere. We need to determine the maximum area on the glass sphere from where the spider can see the fly. The radius of the sphere is assumed to be much larger than the size of the spider and the fly, and the refractive index of the glass is given as √2.

Explanation:
To understand how the spider can see the fly on the glass sphere, we need to consider the concept of refraction. Refraction occurs when light passes through different mediums, such as air and glass, and bends due to the change in the speed of light. In this case, the light from the fly will undergo refraction as it passes through the glass sphere.

1. Angle of Deviation:
The angle of deviation is the angle by which a ray of light is bent when it enters a different medium. It depends on the angle of incidence and the refractive indices of the mediums involved. In this case, the angle of deviation will determine the maximum area on the glass sphere from where the spider can see the fly.

2. Snell's Law:
Snell's law relates the angles of incidence and refraction, and the refractive indices of the two mediums. It is given by the equation: n1 * sin(θ1) = n2 * sin(θ2), where n1 and n2 are the refractive indices, and θ1 and θ2 are the angles of incidence and refraction, respectively.

3. Critical Angle:
The critical angle is the angle of incidence that results in an angle of refraction of 90 degrees. If the angle of incidence exceeds the critical angle, total internal reflection occurs, and the light is reflected back into the original medium. In this case, total internal reflection will prevent the spider from seeing the fly.

4. Calculating the Maximum Area:
To calculate the maximum area on the glass sphere, we need to find the critical angle. The critical angle can be determined using the refractive indices of air and glass. The refractive index of air is approximately 1, and the refractive index of glass is given as √2.

Using Snell's law, we can rearrange the equation to calculate the critical angle: critical angle = arcsin(n2/n1).

For the given scenario, the critical angle can be calculated as follows: critical angle = arcsin(√2/1) ≈ 54.74 degrees.

Considering the glass sphere, the spider will be able to see the fly within a cone-shaped region with the vertex at the center of the sphere. The maximum area on the glass sphere from where the spider can see the fly would be the curved surface area of this cone.

Conclusion:
In conclusion, the maximum area on the glass sphere from where the spider can see the fly is determined by the critical angle of refraction. By calculating the critical angle using the refractive indices of air and glass, we found that the maximum area is within a cone-shaped region on the glass sphere. This cone's curved surface area represents the maximum area from where the spider can see the fly.