JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Geometrical Optics

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Two identical thin biconvex lenses of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled with a liquid of refractive index 1.25. The focal length of the combination is ______ cm.

Answer: 10

Solution

For each biconvex lens with focal length 15 cm:

\frac{1}{f _{1}} = \frac{1}{15} = (1.5 - 1) (\frac{2}{R}) \Rightarrow \frac{1}{R} = \frac{1}{15}

The liquid between the lenses forms a biconcave lens:

\frac{1}{f _{2}} = (1.25 - 1) (\frac{- 2}{R}) = - \frac{0.5}{R} = - \frac{1}{30}

For the combination:

\frac{1}{f _{e q}} = \frac{1}{f _{1}} + \frac{1}{f _{2}} + \frac{1}{f _{1}} = \frac{1}{15} - \frac{1}{30} + \frac{1}{15}

= \frac{2 - 1 + 2}{30} = \frac{3}{30} = \frac{1}{10}

Therefore,

f_{e q} = 10

cm.

JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Integer answer

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