Question

an image 2/3 the size the object is formed by a convex lens at a distance of 12cm from it.find the focal length of the lens.

Answer 1

Let size of object be x cm

∴ A.T.Q. Size of object = 2x/3 cm

Image distance(v) = 12 cm

∴ Object distance(u) = y (Let)

NOTE : Object distance for any type of lens is always negative

∵ Image height / Object height = Image distance / Object distance∴

∴ x ÷ 2x/3 = 12/y

⇒ 2/3 = 12/y

⇒ y = 12×3 /2

⇒ y = 18 cm

∴ Object distance = -18cm(Minus 18 cm)

Using lens formula :

1/v - 1/u = 1/f

∵ Lens is convex and image is real the v will be positive

⇒ 1/12 -(-1/18) = 1/f

⇒1/12 + 1/18 = 1/f

⇒ f = 36/5

⇒ f (focal length) = 7.2cm