Ncert Exercises & Solutions

9.10 What is the focal length of a convex lens of focal length 30cm in contact with a concave lens of focal length 20cm? Is the system a converging or a diverging lens? Ignore the thickness of the lenses.

Hint: $\frac{1}{f_{eff}}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$

Step 1: Find the effective focal length of the combination.
The focal length of the convex lens,

f_{1}

=30cm
The focal length of the concave lens,

f_{2}

= -20cm

Let the focal length of the system of lenses= f
The equivalent focal length of a system of two lenses in contact:

$\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$
$\frac{1}{f} = \frac{1}{30} - \frac{1}{20} = \frac{2 - 3}{60} = - \frac{1}{60}$
$\Rightarrow f = - 60 c m$

Hence, the focal length of the combination of lenses is 60 cm.

Step 2: Determine the system is either converging or diverging.
The negative sign indicates that the system of lenses acts as a diverging lens.

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