The focal length of a sphere with a refractive index gradient is the distance from the center of the sphere to the point where incoming parallel light rays converge after passing through the sphere.
The refractive index gradient determines the rate at which the refractive index changes as you move away from the center of the sphere. This gradient directly affects the curvature of the light rays passing through the sphere, thus impacting the focal length.
Yes, the focal length of a sphere with a refractive index gradient can be calculated using the lens maker's equation, which takes into account the refractive index of the material, the curvature of the sphere, and the refractive index gradient.
The focal length of a sphere with a refractive index gradient is longer than that of a sphere with a constant refractive index. This is because the change in refractive index causes the light rays to bend at different angles, resulting in a longer focal length.
If the gradient becomes steeper, the refractive index changes more rapidly as you move away from the center of the sphere. This causes the light rays to bend at sharper angles, resulting in a shorter focal length.