Question

An effective power of a combination of 5 identical convex lens having focal length f= 20 cm is

Hint:

Always ensure you use the correct sign convention: positive for convex (converging) lenses and negative for concave (diverging) lenses.
Power must be calculated with the focal length strictly in meters, or by using the $100/f$ formula for centimeters.

Answer 1

Step 1: Understanding the Concept:
When multiple thin lenses are placed in close physical contact, the total effective power of the system is the algebraic sum of their individual powers.
A convex lens acts as a converging lens and has a positive focal length, meaning its optical power is also strictly positive.
Step 2: Key Formula or Approach:
The optical power $P$ of a single lens in diopters (D) is given by $P = \frac{100}{f}$ where $f$ is measured in centimeters.
For $n$ identical lenses placed in contact, the total effective power is $P_{\text{eff}} = n \times P$.
Step 3: Detailed Explanation:
The focal length of a single convex lens is given as $f = +20\text{ cm}$.
Calculating the power of one individual lens:
\[ P = \frac{100}{+20} = +5\text{ D} \] Because there are 5 identical lenses placed together in combination, we multiply the single power by 5:
\[ P_{\text{eff}} = 5 \times (+5\text{ D}) = +25\text{ D} \] Step 4: Final Answer:
The effective combined power of the lenses is $+25\text{ D}$.