Variable magnification optical system and imaging apparatus

1. A variable magnification optical system, consisting of a first lens group fixed with respect to the imaging plane and has a positive refractive power, a second lens group having a negative refractive power, a third lens group fixed with respect to the imaging plane and has a positive refractive power, and a fourth lens group having a positive refractive power, arranged in order from the object side, in which magnification is changed by moving the second lens group and focusing is performed by moving the fourth lens group, wherein:

the first lens group consists of a positive lens L 1 p and a cemented lens L 1 c which consists of a negative lens and a positive lens, and has a positive refractive power, arranged in order from the object side;

the third lens group comprises a stop on the most object side;

the fourth lens group consists of a positive lens, a negative lens, and a positive lens, arranged in order from the object side, with at least one surface being an aspherical surface; and

the variable magnification optical system satisfies conditional expressions given below:

3.1< f 1/ fw< 8.0  (1)

0.4< f 1 p/f 1 c< 2.0  (2)

0.3< R 1 c/fw< 0.7  (3)

1.0≦ FNt/FNw< 1.4  (4)

1.5< FNt< 2.3  (5)

where:

f 1 : focal length of the first lens group;

fw: focal length of the entire system at the wide angle end;

f 1 p : focal length of the positive lens L 1 p;

f 1 c : focal length of the cemented lens L 1 c;

R 1 c : radius of curvature of the cemented surface of the cemented lens;

FNt: maximum aperture F-number of the entire system at the telephoto end; and

FNw: maximum aperture F-number of the entire system at the wide angle end.

2. The variable magnification optical system as claimed in claim 1 , wherein the variable magnification optical system satisfies conditional expressions given below:

3.5< f 1/ fw< 5.0  (1-1)

0.8< f 1 p/f 1 c< 1.9  (2-1)

0.35< R 1 c/fw< 0.5  (3-1)

1.0≦ FNt/FNw< 1.3  (4-1)

1.6< FNt< 2.0  (5-1).

3. The variable magnification optical system as claimed in claim 1 , wherein:

the third lens group includes at least a stop, a cemented lens L 3 c which consists of a biconvex lens and a negative lens having a concave surface on the object side with an absolute value of radius of curvature smaller than that of the image side surface, and a negative lens L 3 n having a concave surface on the object side with an absolute value of radius of curvature smaller than that of the image side surface, arranged in order from the object side; and

the variable magnification optical system satisfies conditional expressions given below:

2.2< f 3/ fw< 5.0  (6)

0.3< f 3 c/f 3<2.0  (7)

−2.5< f 3 n/f 3<−0.4  (8)

50<ν dn≦νdp   (9)

where:

f 3 : focal length of the third lens group;

f 3 c : focal length of the cemented lens L 3 c;

f 3 n : focal length of the negative lens L 3 n;

νdp: Abbe number of the positive lens in the cemented lens L 3 c ; and

νdn: Abbe number of the negative lens in the cemented lens L 3 c.

4. The variable magnification optical system as claimed in claim 3 , wherein the variable magnification optical system satisfies conditional expressions given below:

2.5< f 3/ fw< 4.0  (6-1)

0.4< f 3 c/f 3<1.5  (7-1)

−2.0< f 3 n/f 3<−0.5  (8-1)

60<ν dn≦νdp   (9-1).

5. The variable magnification optical system as claimed in claim 1 , wherein:

the second lens group consists of a negative lens L 2 n and a cemented lens L 2 c which consists of a biconcave negative lens and a positive lens, arranged in order from the object side; and

the variable magnification optical system satisfies conditional expressions given below:

0.8<| f 2|/ fw< 1.4  (10)

−0.7<β2 w <−0.3  (11)

0.1< D 12 w/fw< 0.7  (12)

where:

f 2 : focal length of the second lens group;

β 2 w : imaging magnification of the second lens group at the wide angle end; and

D 12 w : distance between the first lens group and the second lens group on the optical axis at the wide angle end.

6. The variable magnification optical system as claimed in claim 5 , wherein the variable magnification optical system satisfies conditional expressions given below:

0.9<| f 2|/ fw< 1.2  (10-1)

−0.6<β2 w<− 0.4  (11-1)

0.2< D 12 w/fw< 0.6  (12-1).

7. The variable magnification optical system as claimed in claim 1 , wherein:

the fourth lens group consists of a biconvex lens, a negative lens having a concave surface on the image side with an absolute value of radius of curvature smaller than that of the object side surface, and a positive lens, arranged in order from the object side; and

the variable magnification optical system satisfies a conditional expression given below:

1.2< f 4/ fw< 2.6  (13)

where,

f 4 : focal length of the fourth lens group.

8. The variable magnification optical system as claimed in claim 7 , wherein the variable magnification optical system satisfies a conditional expression given below:

1.5< f 4/ fw< 2.2  (13-1).

9. An imaging apparatus, comprising the variable magnification optical system as claimed in claim 1 .