A convex lens made of glass has two surfaces of rad of curvature 10cm and 12cm respectively its focal length is 10cm Calculate its refractive index. Also calculate the focal length of the lens when it is immersed in (a) water ( 4.5) and (b) carbon di sulphide ( 1.65)
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The value of focal length for water is f = 5.71 cm and for Carbon di sulphide is 30.7 cm
Explanation:
(a) Immersed in water:
1 / f = ( n2 / n1 - 1 ) ( 1/R1 - 1/R2)
1 / f = ( 4.5 - 1 ) ( 1 / 10 - 1 / 20)
1 / f = ( 3.5 ) ( 2 - 1 / 20 )
1 / f = 3.5 x 1 / 20
1/ f = 0. 175
f = 1/ 0.175 = 5.71 cm
(b) Carbon di sulphide
1 / f = ( n2 / n1 - 1 ) ( 1/R1 - 1/R2)
1 / f = ( 1.65 - 1 ) ( 1 / 10 - 1 / 20)
1 / f = ( 0.65 ) ( 2 - 1 / 20)
1/f = 0.65 / 20 = 0.0325
f = 1 / 0.0325
f = 30.7 cm
Thus the value of focal length for water is f = 5.71 cm and for Carbon di sulphide is 30.7 cm
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