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Q. A thin convex lens of focal length $10 cm$ is placed in contact with the concave lens of same material and of same focal length. The focal length of combination will be:

Ray Optics and Optical Instruments

Solution:

According to the relation
$\frac{1}{ f }=\frac{1}{ f _{1}}+\frac{1}{ f _{2}}$
$f =\frac{ f _{1} f _{2}}{ f _{1}+ f _{2}}$
$=\frac{10 \times(-10)}{10+-10}$
$=\frac{-100}{0}=\infty$