When the gap between two identical concave thin lenses `(mu=(3)/(2), f=10cm)` placed in contact is filled with certain liquid, the image of an object placed at 15 cm from lens combination shifts away from the lens by `5//4` cm. If the refractive index of liquid is `mu`, then write `3mu` as your answer.

Answer

4

Explanation

In case (i) (without liquid)

`1/v = 1/(-15) = 2/f`
`rArr 1/v = -1/5 - 1/15 = -4/15`
`rArr v = -3.75 cm`
When the gap is filled with liquid
`v. = - 3.75 - 1.25 = - 5 cm`
`-1/5 -1/(-15) = -1/5 + (mu_(l)-1) (2/R)`
Here, `1/10 = (3/2-1) (2/R) rArr R = 10 cm`
Hence, `-2/15 = -1/5 + (mu_(l)-1)/5`
`rArr mu_(l) = 4/3`