A thin glass (refractive index 1.5) lens has optical power of `-5D` in air. Its optical power in a liquid medium with refractive index 1.6 will be

Options

A. `25 D`
B. `-1 D`
C. `1D`
D. `-25D`

Answer

C

Explanation

`(1)/(f_(e))=(mu-1)((1)/(R_(1))-(1)/(R_(2)))`
`=(1.5-1)((1)/(R_(1))-(1)/(R_(2)))` ...(i)
and `(1)/(f_(m))=((mu_(g)-mu_(m))/(mu_(m)))((1)/(R_(1))-(1)/(R_(2))) `
`(1)/(f_(m))=((1.5)/(1.6)-1)((1)/(R_(1))-(1)/(R_(2)))` ....(ii)
Thus, `(f_(m))/(f_(a))=((1.5-1))/(((1.5)/(1.6)-1))=-8`
`f_(m)-8xxf_(a)`
`=-8xx(-1)/(5)` `( :'f_(a)=(1)/(p)=-(1)/(5)m)`
`=1.6m`
`:. P_(m)=(mu)/(f_(m))=(1.6)/(1.6)=1D`