A needle placed `45 cm` from a lens forms an image on the screen placed `90` cm on the other side of the lens. Identify the type of the lens and determine its focal length. What is the size of the image if the size of needle is `5.0 cm` ?

Answer

convex ; `30 cm, -10 cm

Explanation

Here, `u = -45 cm, v = 90 cm, f = ?, h_(1) = 5.0 cm, h_(2) = ?`
From `(1)/(f) = (1)/(v) - 1/u, (1)/(f) = 1/90 + 1/45 = (1+2)/(90) = (3)/(90) = 1/30`
`f = 30 cm`
As f is positive, the lens must be convex.
From `(h_(2))/(h_(1)) = v/u, h_(2) = (v)/(u) xx h_(1) = (90)/(-45) xx 5.0 = -10 cm`
As `h_(2)` is negative, the image is inverted.