Combination of Lenses and Sample Examples

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/f1(Cm) and addition of one divided by the length of object1/f2(cm)  in centimeter and addition of the distance d(cm) in centimeter and divided by the final length fn(cm) in centimeter. Hence the combination of lenses formula can be written as

1/F(cm)=1/f1(Cm)+1/f2(cm)+……+d(cm)/fn(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/f1+1/f2…….3

1/v-1/u =1/f…..4

From equations 3 and 4

1/F=1/f1+1/f2

1/F=1/f1+1/f2+…..+1/fn

1/F=1/f1+1/f2+……+d/fn

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.

F1=+8cm for convex lens

F2=20 cm for concave lens

The focal length of this combination is given by

1/F=1/f1+1/f2

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:

F1=18cm

F2=20cm

D=6cm

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

1/F=1/f1+1/f2-d/f1.f2

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

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