The power of a combination of two lenses X and Y is 5D. If the focal length of lens X be 15cm:
  1. Calculate the focal length of lens Y.
  2. State the nature of lens Y.
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  1. $\text{P}=\text{P}_\text{x}+\text{P}_\text{y}$
$\text{P}=\frac{1}{\text{f}_\text{x}}+\frac{\text{1}}{\text{f}_\text{y}}$

$5=\frac{100}{15}+\frac{\text{1}}{\text{f}_\text{y}}$

$\frac{\text{1}}{\text{f}_\text{y}}=5-\frac{100}{15}$

$=\frac{-25}{15}$

${\text{f}_\text{y}}=-0.6\text{m}=-60\text{cm}$
  1. Lens Y is a concave lens since it has negative focal length.
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