### Combination of Lenses Formula :

Combination of lenses formula is one divided by final length1/F_{(cm)} in centimeter is equal to the one divided by the length of object 1/f_{1(Cm)} and addition of one divided by the length of object1/f_{2(cm) }** **in centimeter and addition of the distance d_{(cm)} in centimeter and divided by the final length f_{n(cm)} in centimeter. Hence the combination of lenses formula can be written as

1/F_{(cm)}=1/f_{1(Cm)}+1/f_{2(cm)}+……+d_{(cm)}/f_{n(cm)}

1/V1-1/u=1/f1……1

For the final image I produced by the second lens N

1/v-1/v1 =1/f2……2

Adding equations 1 and 2

1/v -1/u =1/f_{1}+1/f_{2}…….3

1/v-1/u =1/f…..4

From equations 3 and 4

1/F=1/f_{1}+1/f_{2}

1/F=1/f_{1}+1/f_{2}+…..+1/f_{n}

1/F=1/f_{1}+1/f_{2}+……+d/f_{n}

### Sample Examples :

### Example:1

Calculate lens combination’s focal length? In a convex lens with a focal length of 8cm interferes with a concave lens with a focal length of 20cm.

### Answer:

Given that.

F_{1}=+8cm for convex lens

F_{2}=20 cm for concave lens

The focal length of this combination is given by

1/F=1/f_{1}+1/f_{2}

1/F=1/8+1/20

1/F=9/160

F=0.056

Hence, the total focal length of this combinations is +0.056 cm

### Example:2

Calculate the combination’s focal length ? In a distance of 6cm separates two narrow convex lenses with focal lengths of 18cm and 20cm.

### Answer:

F_{1}=18cm

F_{2}=20cm

D=6cm

The focal length of this combination is F, is given by

1/F=1/f_{1}+1/f_{2}-d/f_{1}.f_{2}

1/F=1/18+1/20-6/18*20

=1/18+1/20-6/360

=1/18+1/20-60

=38/60

=0.63cm

Hence, the total focal length of this combination is 0.63 cm