Variable focal length optical system

1. A variable focal length optical system used in combination with an infinity corrected objective lens, the variable focal length optical system comprising:

an imaging lens configured to condense a parallel beam of light from the objective lens to form an intermediate image;

a relay system comprising, in sequence from an object side, a first relay lens and a second relay lens, the relay system configured to relay the intermediate image to infinity; and

a lens system of a liquid resonant type which is located between the first relay lens and the second relay lens, the lens system having a refractive index that changes in response to an inputted drive signal, wherein

a front principal point of the lens system is located to be conjugated with an exit pupil of the objective lens, and

with f Tube denoting a focal length of the imaging lens and f R1 denoting a focal length of the first relay lens, an expression (1) below is satisfied,

1.90< f Tube /f R1 ≤2.15  (1).

2. The variable focal length optical system according to claim 1 , wherein

with X denoting a distance from a front end surface of the lens system to the front principal point of the lens system, an expression (2) below is satisfied,

X<f R1 ≤2 X   (2).

3. The variable focal length optical system according to claim 1 , wherein

with f R2 denoting a focal length of the second relay lens and f obj1x denoting a focal length of the objective lens with 1× magnification, an expression (3) below is satisfied,

f R2 =f obj1x ×f R1 /f Tube   (3).