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Question

Two thin lenses of power +2.5D and -0.5D are placed in contact. Find the power of the lens combination. Also, calculate the focal length of the combination.


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Solution

Step 1: Given data,

Power of lens 1 is P1=+2.5D

Power of lens 2 is P2=-0.5D

Step 2: Finding the power of the lens combination,

According to power of lens combination formula,

P=P1+P2

Substituting the know values,

P=+2.5D+-0.5DP=2.5-0.5P=+2D

Thus, the power of the lens combination is +2D.

Step 3: Finding the focal length of lens 1,

According to the power of lens formula,

P1=1f1

where f1 is the focal length of the lens 1

Substituting the known values,

+2.5D=1f12.5=1f1f1=12.5f1=0.4m

Thus, the focal length of lens 1 is 0.4m.

Step 4: Finding the focal length of lens 2,

According to the power of lens formula,

P2=1f2

where f2 is the focal length of the lens 1

Substituting the known values,

-0.5D=1f2-0.5=1f2f2=-10.5f2=-2m

Thus, the focal length of the lens 2 is 2m.

Step 5: Finding the focal length of the lens combination,

According to the focal length of the lens combination formula,

1f=1f1+1f2

where, f is the focal length of lens combination.

Substituting the known values,

1f=10.4m+1-2m1f=10.4-121f=2f=12f=+0.5mf=+50cm

Thus, the focal length of the lens combination is +50cm.


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