CGPET 2021 Solved Paper

According to given situation, formation of image from convex lens is shown below

(∵AB=A′B′)
Here, u=−2f=−d(let)
∴ f=

d

2

By lens Maker's formula,

1

f

=(aµg−1)(

1

R1

−

1

R2

)
⇒

1

f

=(aµg−1)(

1

R

−

1

(−R)

)
⇒

1

f

=(aµg−1).

2

R

⇒

1 d

2

=(1.5−1).

2

R

⇒d=2R
When object and convex lens are immersed in liquid, then the image formed two times enlarged than object.
m=−

v

u

⇒1=−

v

u

∴ v=-2u
But object remains at distance, u=−d.
Consider, then the focal length of lens in liquid becomes f1, then

1

f1

=

1

v

−

1

u

⇒f1=

1

−2u

−

1

u

⇒ f1=

2d

3

(∵u=−d)
Let refractive index of liquid is µl ,

1

f1

=(

aµg

aµl

−1).

2

R

1

2d 3

=(

1.5

µl

−1).

2

d 2

After solving, µl=

12

11