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What is the power of this combination of lens placed together when the power of the converging lens is 4.50┬аD and diverging lens is 3.00┬аD?
13.5D
+1.5D
5D
7.5D
+1.5D
When two or more thin lenses are placed in contact, the total power (P) of the combination is the algebraic sum of the individual powers of the lenses. A converging lens (convex) has positive power, and a diverging lens (concave) has negative power.
When two or more thin lenses are placed in contact, the total power (P) of the combination is the algebraic sum of the individual powers of the lenses. A converging lens (convex) has positive power, and a diverging lens (concave) has negative power.
Think of it like adding gains and losses: the convex lens adds light-bending strength (+4.5), while the concave lens subtracts it (-3.0), resulting in a net bending strength.
PtotalтАЛ=P1тАЛ+P2тАЛ+...+PnтАЛ тАФ The principle of addition of powers for thin lenses in contact
P=f1тАЛ тАФ Power definition where f is the focal length in meters
The total focal length (F) of combined lenses in contact is given by 1/F=1/f1тАЛ+1/f2тАЛ. Since power P is defined as 1/f (in meters), the powers add linearly: PtotalтАЛ=P1тАЛ+P2тАЛ. Here, P1тАЛ=+4.50┬аD (converging) and P2тАЛ=тИТ3.00┬аD (diverging).
Converging lenses are assigned a positive (+) power sign.
Diverging lenses are assigned a negative (-) power sign.
The SI unit of optical power is the Dioptre (D).
Allows for compound lens systems to achieve specific focal lengths in cameras and eyewear.
Spectacles for correcting refractive errors (myopia/hypermetropia).
Microscopes and telescope objectives.
Power of Converging lens (P1тАЛ) = +4.50 D
Power of Diverging lens (P2тАЛ) = -3.00 D
Calculation: PtotalтАЛ=(+4.50)+(тИТ3.00)=+1.50┬аD
B is correct тАФ The power of the combination is the sum of the individual powers, which equals +1.50 D.
Always verify the sign convention: convex is always positive, and concave is always negative, regardless of the relative values.
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