Question

A combination of $3$ convex lenses is made. The focal length of lens I is $+5cm$, lens II is $+10cm$ and lens III is $+20cm$. Calculate the total power of the combination in dioptre?

• A. 35

Answer 1

The correct option is A 35

Given, focal length of lens I = $+5cm$, focal length of lens II =$+10cm$ and focal length of lens III = $+20cm$.
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 ${\text{P}}_{\text{t}}={\text{P}}_I$ + ${\text{P}}_{II}$ + ${\text{P}}_{III}$ ;

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

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

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