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Two thin lenses of focal length f(1) and...

Two thin lenses of focal length `f_(1)` and `f_(2)` are in contact and coaxial. The power of the combination is

A

`sqrt(f_(1)/f_(2)`

B

`sqrt(f_(2)/f_(1)`

C

`(f_(1)+f_(2))/2`

D

`(f_(1)f_(2))/f_(1)f_(2)`

Text Solution

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The correct Answer is:
To find the power of the combination of two thin lenses in contact and coaxial, we can follow these steps: ### Step 1: Understand the Concept of Power The power \( P \) of a lens is defined as the reciprocal of its focal length \( f \): \[ P = \frac{1}{f} \] where \( P \) is measured in diopters (D) and \( f \) is in meters. ### Step 2: Determine the Power of Each Lens For two lenses with focal lengths \( f_1 \) and \( f_2 \): - The power of the first lens \( P_1 \) is: \[ P_1 = \frac{1}{f_1} \] - The power of the second lens \( P_2 \) is: \[ P_2 = \frac{1}{f_2} \] ### Step 3: Combine the Powers When two lenses are in contact and coaxial, the total power \( P \) of the combination is the sum of the individual powers: \[ P = P_1 + P_2 \] Substituting the expressions for \( P_1 \) and \( P_2 \): \[ P = \frac{1}{f_1} + \frac{1}{f_2} \] ### Step 4: Simplify the Expression To combine the fractions, we can find a common denominator: \[ P = \frac{f_2 + f_1}{f_1 f_2} \] ### Step 5: Final Result Thus, the power of the combination of the two lenses is: \[ P = \frac{f_1 + f_2}{f_1 f_2} \]
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