A spherical glass bottle having negligible wall thickness is placed in air. When the bottle is completely filled with water, its focal length is f . If the water is replaced by another transparent liquid of higher refractive index, then the focal length changes to f' . Then the correct option is

Step-by-step solution

The spherical glass bottle with negligible wall thickness filled with liquid acts as a solid liquid sphere of radius R . The system can be considered as a thick lens with two spherical refracting surfaces of radius R and -R , separated by a distance t = 2R . The power of the first surface is P₁ = - 1 R and the second surface is P₂ = 1 - -R = - 1 R . The equivalent power of the spherical lens is given by: P = P₁ + P₂ - t P₁ P₂ P = 2( - 1) R - 2R ( - 1 R )^2 P = 2( - 1) R ( 1 - - 1 ) = 2( - 1) R The focal length f is