• The power of a thin convex lens of glass is 5D. When it is immersed in a liquid, then it behaves like a divergent lens of focal length 100 cm. Calculate the refractive index of the liquid. The refractive index of glass is 1.5.

The focal length of the think convex lens fair = 1/5 = 0.2 m = + 20 cm (convex lens)

In the liquid, the focal length fliquid = -100 cm (Diverging lens)

Using lens maker's formula for lens in air,

1/fair = (nglass-1)(1/R1 - 1/R2)

1/fair = (1.5 - 1)(1/R1 - 1/R2)

1/fair = 0.5(1/R1 - 1/R2)  ----> I

Using Lens makers formula for lens in liquid,

1/fliquid  = (nglass/nliquid - 1)(1/R1 - 1/R2)

1/fliquid = (1.5/nliquid - 1)(1/R1 - 1/R2) ------->II

Dividing equation II by I

fair/fliquid = (1.5/nliquid - 1)/0.5

+20/-100 = (1.5/nliquid - 1)/0.5

-1/5 = ​(1.5/nliquid - 1)/0.5

-0.5/5 = 1.5/nliq
uid - 1

-0.1 = ​1.5/nliquid - 1

0.9 = 1.5/nliquid

Therefore,

nliquid = 1.5/0.9 = 1.67

 

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