An object is placed vertically at a distance of 20 cm from a convex lens .If the height of the object is 5 cm and the focal length of the lens is 10 cm, what will be the position, size and nature of the image? How much bigger will the image be as compared to the object?

Explanation

Height of the object `(h_1) = 5` cm,
focal length (f) = 10 cm,
distance of the object (u) = - 20 cm
Image distance (v) = ?,
Height of the image `(h_2) = ?`
Magnification (M) = ?
`1/v -1/u =1/f`
`1/v =1/u+1/f`
`1/v =1/(-20) +1/10`
`1/v = (-1+2)/20`
`1/v =1/20`
`v = 20 cm`
The positive sign of the image distance i shows that image is formed at 20 cm on the other side of the lens.
Magnification `(M) = (h_2)/(h_1) = v/u`
`h_2 = v/u xxh_1`
`h_2 = (20)/(-20) xx5`
`h_2 = (-1) xx5`
`h_2 = -5 cm`
`M = u/v = (20)/(-20)=-1`
The negative sign of the height of the image and the magnification shows that the image is inverted and real. It is below the principal axis and is of the same size as the object.
2. The focal length of a convex lens is 20 cm. What is its power? Given: Focal length = f = 20 cm = 0.2 m
Power of the lens =P= ?
`P = 1/(f(m)) =1/(0.2)=5D`
The power of the lens is 5 D.