A plano-covex lens is made of a material of refractive index n. When a small object is placed 30cm away in front of the curved surface of the lens, an image of double the size of the object is produced. Due to reflection from the convex surface of the lens, another faint image is observed at a distance of 10 cm away from the lens. Which of the following statement (s) is (are) true?

Options

A. The refractive index of the lens 2.5
B. The radius of curvature of the convex surface is 45 cm
C. The faint image is erect and real
D. The focal length of the lens is 20 cm

Answer

A, D

Explanation

For lens
`(1)/(v)-(1)/(u)=(1)/(f)implies(1)/(v)-(1)/(-30)=(1)/(f)`
Also `m=(v)/(u)implies-2=(v)/(u)`
On solving we get `f=+20 cm` and `v=60 cm`.
For reflection
`(1)/(v)+(1)/(u)=(1)/(f)=(2)/(R)implies(1)/(10)+(1)/(-30)=(2)/(R)impliesR=30` cm
The image formed by convex side is faint erect and virtual. By lens makes formula
`(1)/(f)=((n_(l))/n_(s)-1)((1)/(R_(1))-(1)/(R_(2)))`
`:'``(1)/(20)=((n_(l))/(1)-1)((1)/(30))``:'``n_(l)=2.5`