Find the radii of curvature of the two surfaces of a convex lens used as a simple microscope, whose maximum magnifying power is $6$ . Refractive index of the material of the lens is $μ_{l} = 1.5$ and the radii of both spherical surfaces of the lens are equal.

2 cm

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6 cm

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3 cm

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5 cm

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Solution

The correct option is D $5 cm$
Given, $M P = 6$
Maximum magnifying power is, $M P_{m a x} = 1 + \frac{D}{f}$
$\Rightarrow 6 = 1 + \frac{25}{f}$
$∴ f = 5 cm$

According to lens-maker's equation, $\frac{1}{f} = \frac{μ_{l} - μ_{s}}{μ_{s}} (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

For the given lens, $R_{1} = R_{2} = R$

$\frac{1}{5} = \frac{1.5 - 1}{1} (\frac{1}{R} - (- \frac{1}{R}))$
$\frac{1}{5} = 0.5 \times \frac{2}{R}$
$∴ R = 5 cm$

Hence, $(D)$ is the correct answer.

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Find the radii of curvature of the two surfaces of a convex lens used as a simple microscope, whose maximum magnifying power is 6. Refractive index of the material of the lens is μl=1.5 and the radii of both spherical surfaces of the lens are equal.

The correct option is D 5 cmGiven, MP=6 Maximum magnifying power is, MPmax=1+Df ⇒6=1+25f ∴f=5 cm According to lens-maker's equation, 1f=μl−μsμs(1R1−1R2) For the given lens, R1=R2=R 15=1.5−11(1R−(−1R)) 15=0.5×2R ∴R=5 cm Hence, (D) is the correct answer.

Find the radii of curvature of the two surfaces of a convex lens used as a simple microscope, whose maximum magnifying power is $6$ . Refractive index of the material of the lens is $μ_{l} = 1.5$ and the radii of both spherical surfaces of the lens are equal.