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?

Answer

AD

Explanation

For lens

`(1)/(v) - (1)/(u) = (1)/(f)`
`(1)/(60) - (1)/((-30)) = (1)/(f') implies f' = 20 cm `
Also `(1)/(f) = (n-1)((1)/(R) - (1)/(oo)) = ((n-1))/(R) …… (ii)`
For reflection from convex mirror (curved surface)

`(1)/(v) + (1)/(u) = (1)/(f') = (2)/(R)`
`(1)/(+10) + (1)/(-30) = (1)/(f') = (2)/(R) ....... (iii)`
`R = 30 cm`
from (i) , (ii) & (iii)
n = 2.5 ,
faint image erect & virtual