Question

A combination of 3 convex lenses is arranged as shown. The focal length of lens I is +5 cm, lens II is +10 cm and lens III is +20 cm. Calculate the total power of the combination of the lens?

• A. -35 D
• B. +1 D
• C. + 35 D
• D. + 75 D

Answer 1

The correct option is C + 35 D

Given, focal length of lens I = +5 cm, focal length of lens II = +10 cm and focal length of lens III = +20 cm. Since all the units are in cm, to convert in metres the formula for power becomes,

Power of lens $P=\frac{1}{\text{focal length in m}}=\frac{100}{\text{focal length in cm}}$.

Total Power = ${\text{P}}_I$ + ${\text{P}}_{II}$ + ${\text{P}}_{III}$ ; P = $\frac{1}{\text{f}}$

So, ${\text{P}}_I$ = $\frac{100}{5}$ D ; ${\text{P}}_{II}$ = $\frac{100}{10}$ D ; ${\text{P}}_{III}$ = $\frac{100}{20}$ D

Total Power of combination ${\text{P}}_{\text{t}}={\text{P}}_I$ + ${\text{P}}_{II}$ + ${\text{P}}_{III}$ ;

${\text{P}}_{\text{t}}=\frac{100}{5}$ + $\frac{100}{10}$ + $\frac{100}{20}$ = $\frac{700}{20}$

${\text{P}}_{\text{t}}$ = + 35 D.

Therefore, the total power of combination is + 35 D.