Diameter of a plano-convex lens is 6 cm and thickness at the centre is 3 mm. If the speed of light in the material of the lens is 2×108 m/sec, the focal length of the lens is
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Here
v = 2×108 ms-1
c = 3×108 ms-1
µ= c/v = 1.5
D = 6 cm = 60 mm
Radius = 30 mm
Here we have to find the radius of the surface of the lens
O is the centre of the circle
So AC is the chord of the circle
By Pythagora’s theorem
R2 = 302 + (R-3)2
=> R2 = 900 + R2 – 6R + 9
=> 909 – 6R = 0
=> R = 151.5
R1 = 151.5 mm
R2 = ∞ (for plano convex lens one side is a plane)
By lens makers formula
1/f = (µ-1)(1/R1 – 1/R2)
=> 1/f = (1.5 -1) (1/151.5 – 1/∞)
=> 1/f = 0.5×1/151.5
=> 1/f = 1/303
=> f = 303 mm
=> f = 30.3 cm ≈ 30 cm
v = 2×108 ms-1
c = 3×108 ms-1
µ= c/v = 1.5
D = 6 cm = 60 mm
Radius = 30 mm
Here we have to find the radius of the surface of the lens
O is the centre of the circle
So AC is the chord of the circle
By Pythagora’s theorem
R2 = 302 + (R-3)2
=> R2 = 900 + R2 – 6R + 9
=> 909 – 6R = 0
=> R = 151.5
R1 = 151.5 mm
R2 = ∞ (for plano convex lens one side is a plane)
By lens makers formula
1/f = (µ-1)(1/R1 – 1/R2)
=> 1/f = (1.5 -1) (1/151.5 – 1/∞)
=> 1/f = 0.5×1/151.5
=> 1/f = 1/303
=> f = 303 mm
=> f = 30.3 cm ≈ 30 cm
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