A plano convex lens made of transparent material having refractive index 53, has a maximum thickness of 1 mm. If the diameter of its aperture is 4 cm. Its focal length in air (in cm) is_______

Rsinθ=2cm R(1-cosθ)=0.1 cm sinθ1-cosθ=20 2sinθ2cosθ22.cos2θ2=20 tanθ2=20 sinθ2tanθ21+tan2θ2=40401 R=2×40140≅20cm 1f=(53−1)×120 f=30 cm

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A plano convex lens made of transparent material having refractive index $\frac{5}{3}$ , has a maximum thickness of 1 mm. If the diameter of its aperture is 4 cm. Its focal length in air (in cm) is_______

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answer is 30.

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Detailed Solution

$R \sin θ = 2 c m$
$R (1-cosθ) =0.1 cm$
$\frac{sinθ}{1-cosθ} =20$
$\frac{2sin \frac{θ}{2} \cos \frac{θ}{2}}{{2.cos}^{2} \frac{θ}{2}} =20$
$\tan \frac{θ}{2} = 20$
$\sin θ \frac{2 \tan \frac{θ}{2}}{1 + \tan^{2} \frac{θ}{2}} = \frac{40}{401}$
$R = \frac{2 \times 401}{40} ≅ 20 c m$
$\frac{1}{f} = (\frac{5}{3} - 1) \times \frac{1}{20}$
$f = 30 c m$