A converging lens made of crown glass (refractive index 1.5) has focal length 20cm in air. If it is immersed in a liquid of refractive index 1.6,its focal length will be ......
Answers
The new focal length is 58.125 cm.
Explanation:
Case 1:
Let the focal length of lens in air be f(air):
Given that:
fair = 20 cm , n1 = 1 , n2 = 1.5 (glass)
According to formula:
1/f (air) = [ n2 / n1 - 1 ] [ 1/R1 - 1/R2]
1/20 = [ 1.5 / 1 - 1 ] [1/R1 - 1/R2]
1/20 = 0.5 [1/R1 - 1/R2]
Case 2:
Focal length in water be f(water).
n1 = 1.33 , n2 = 1.5
According to lens formula:
1/f (water) = [ n2 / n1 - 1 ] [ 1/R1 - 1/R2]
1/f (water) = [ 1.55 / 1.33 - 1 ] [ 1/R1 - 1/R2]
1/f (water) = 0.128 [ 1/R1 - 1/R2]
Dividing (1) by (2) we get:
f(water) / 20 = 0.5 / 0.128
f(water) = 0.5 / 0.128 x 20
f(water) = 78.125 cm
New focal length = 78.125 cm - 20 cm = 58.125 cm
Thus the new focal length is 58.125 cm.
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