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The power of a lens (biconvex) is $1.25 \mathrm{~m}^{-1}$ in particular medium. Refractive index of the lens is 1.5 and radii of curvature are $20 \mathrm{~cm}$ and $40 \mathrm{~cm}$ respectively. The refractive index of surrounding medium:

Option: 1
$1.0$

Option: 2
$\frac{9}{7}$

Option: 3
$\frac{3}{2}$

Option: 4
$\frac{4}{3}$

Answers (1)

best_answer

$\mathrm{P=1.25m^{-1}}$

$\mathrm{\mu =1.5}$

$\mathrm{R_{1}=20cm,R_{2}=40cm}$

$\mathrm{P=\frac{1}{f} =\left(\mu_g^n-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right) }$

$\mathrm{\mu_g^m =\frac{\mu_g}{\mu_m}=\frac{1.5}{\mu_m} }$

$\mathrm{P =\left(\frac{1.5}{\mu_m}-1\right)\left(\frac{1}{+20}-\frac{1}{(-40)}\right) }$

$\mathrm{\frac{5}{4} =\left(\frac{1.5}{\mu_m}-1\right)\left(\frac{3}{40 \times 10^{-2}}\right) }$

$\mathrm{\frac{1}{6} =\frac{1.5}{\mu_m}-1 }$

$\mathrm{\frac{7}{6} =\frac{1.5}{\mu_m} }$

$\mathrm{\mu_m =\frac{9}{7}}$

Hence 2 is correct option.

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