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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 `=5implies f=20 cm`
`(1)/(f ) = ((mu_g - mu_a)/(mu_a)) ((1)/(R_1) -(1)/(R_2))implies (1)/(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))implies 1-(1.5 )/(mu_l) =(1)/(10) implies (9)/(10) = (3)/( 2mu_l)`
` implies mu_l =5/3`
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