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The radii of curvature of a double conca...

The radii of curvature of a double concave lens are 30 cm and 45 cm. What is its focal length in water ?
`[""_(a)n_(g)=1.5, ""_(a)n_(w)=4//3]`

A

`-144 cm`

B

`-130 cm `

C

`-114 cm `

D

`-100 cm `

Text Solution

Verified by Experts

The correct Answer is:
A
In this problem, we have to find,
`" "_(w)n_(g)=(""_(a)n_(g))/(""_(a)n_(w))=(3//2)/(4//3)=(9)/(8)`
`therefore` For a concave lens, `R_(1)` is -ve and `R_(2)` is +ve.
`therefore (1)/(f)=(""_(w)n_(g)-1)((1)/(R_(1))-(1)/(R_(2)))`
`=((9)/(8)-1)xx(-(1)/(30)-(1)/(45))`
`= -(1)/(8) xx ((1)/(30)+(1)/(45))`
`= -(1)/(8)xx(1)/(18)= -(1)/(144)`
`therefore f=-144 cm`
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