NEET 2023, Physics Q31: Thin Lens and Mirrors

NEET2023Physics

In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin)?

Solution

Treat the system as three thin lenses in contact: two plano-concave liquid lenses (one on each side) and one biconvex glass lens.

Using the lensmaker's formula $\frac{1}{f} = (n - 1) (\frac{1}{R _{1}} - \frac{1}{R _{2}})$ with appropriate sign conventions:

Left liquid lens ( $n = 1.6$ ): $\frac{1}{f _{1}} = (1.6 - 1) (\frac{1}{\infty} - \frac{1}{- 20}) = - \frac{3}{100}$ (after sign analysis).

Glass lens: $\frac{1}{f _{2}} = (1.5 - 1) (\frac{1}{20} - \frac{1}{- 20}) = \frac{1}{20}$ .

Right liquid lens: $\frac{1}{f _{3}} = - \frac{3}{100}$ .

$\frac{1}{f _{e q}} = - \frac{3}{100} + \frac{5}{100} - \frac{3}{100} = - \frac{1}{100}$

$∴ f_{e q} = - 100$ cm.

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