Diameter of a Plano-convex lens is 6 cm and the thickness at the center is 3 mm. If the speed of light in the material of the lens is 2 x 10^8 m/sec, what is the focal length of the lens?

Question

vikas askiitian expert · Answer

diameter = 2 Radius (R)

2R = 6

R = 3cm

1/f = (u-1)/R ......1

this is the relation bw focal length of plano convex lens & u(refractive index) ...

u = c/v = 3*10⁸/2*10⁸ = 1.5

now put u in eq 1 , will get focal length

vineet jakhar · Answer

radius will be 15 not 3! use geometry. let (x) be radius of curvature .BASE- (x-3) HEIGHT -(3) HYPOTANEOUS -(x) solve and get (x)! :)

ankit singh · Answer

from right angled ∆OAB, OA² = AB² + BO² ⇒R² = (radius)² + (radius - thickness)² ⇒R² = 3² + (R - 0.3)² ⇒R² = 9 + R² - 0.6R + 0.09 ⇒0.6R = 9.009 ⇒R = 90.09/6 ≈ 15 cm it is given that, speed of light in material of lens is 2 × 10^ 8m/s so, refractive index, μ = 3 × 10^8/2 × 10^8 = 1.5 now using formula, 1/f = (μ - 1)[1/R1 - 1/R2] here, R1 = 15cm , R2 = ∞ so, 1/f = (1.5 - 1)[1/15 - 1/0] = 0.5/15 = 1/30 hence, f = 30 cm

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Diameter of a Plano-convex lens is 6 cm and the thickness at the center is 3 mm. If the speed of light in the material of the lens is 2 x 10^8 m/sec, what is the focal length of the lens?

Diameter of a Plano-convex lens is 6 cm and the thickness at the center is 3 mm. If the speed of light in the material of the lens is 2 x 10^8 m/sec, what is the focal length of the lens?

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