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A convex glass lens of focal length 20 c...

A convex glass lens of focal length 20 cm and refractive index 1.5 is immersed in water of R.I. `4//3`. What is the change in its focal length ?

A

30 cm

B

40 cm

C

50 cm

D

60 cm

Text Solution

Verified by Experts

The correct Answer is:
D
When it is immersed in water, the rays of light will travel from water to glass. Hence we calculate
`" "_(w)n_(g)=(""_(a)n_(g))/(""_(a)n_(w))=(3//2)/(4//3)=(9)/(8)`
`therefore (1)/(f_(w))=(""_(w)n_(g)-1) ((1)/(R_(1))-(1)/(R_(2))) " " `...(1)
and `(1)/(f_(a))=(""_(a)n_(g)-1)((1)/(R_(1))-(1)/(R_(2))) " " ` ...(2)
`therefore` Dividing (1) by (2), we get
`therefore (f_(a))/(f_(w)) =((""_(w)n_(g)-1))/((""_(a)n_(g)-1))=((9)/(8)-1)/((3)/(2)-1)=((1)/(8))/((1)/(2))=(1)/(4)`
`therefore f_(w)=4f_(a)=4 xx 20 = 80 cm`
`therefore ` Change of focal length `=f_(w)-f_(a)=80-20=60 cm`
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