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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?



Grade:12

3 Answers

vikas askiitian expert
509 Points
13 years ago

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
33 Points
5 years ago
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
askIITians Faculty 614 Points
3 years ago
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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