Diameter of a plano - convex lens is 6cm and thickness at the centre is 3mm. If speed of light in material of lens is 2×108m/s, the focal length of the lens is :
(1)15cm(2)20cm(3)30cm(4)10cm
Answers
focal length of plano - convex lens would be 30cm
see figure, a plano-convex lens of diameter 6cm and thickness at the centre is 3mm is shown in figure.
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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