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A thin convergent glass lens (mug=1.5) h...

A thin convergent glass lens `(mu_g=1.5)` has a power of `+5.0D.` When this lens is immersed in a liquid of refractive index `mu_1,` it acts as a divergent lens of focal length `100 cm.` The value of `mu_1` is

A

`4//3`

B

`5//3`

C

`5//4`

D

`9//5`

Text Solution

Verified by Experts

The correct Answer is:
B
Power =5 `rArrf=20cm`
`1/f=((mu_(g)-mu_(a))/(mu_(a)))(1/(R_(1))-1/(R_(2)))rArr1/20=((1.5)/1-1)(1/(R_(1))-1/(R_(2)))` …(i)
and `1/(-100)=((1.5-mu_(l))/(mu_(l)))(1/(R_(1))-1/(R_(2)))` …(ii)
Dividing I by II we get `-5=(1/2)/(((1.5)/(mu_(l))-1))rArr1-(1.5)/(mu_(l))=1/10rArr9/10=3/(2mu_(l))`
`rArrmu_(l)=5/3`
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