An object of height 4 cm is placed at a distance of 30 cm from the optic centre of a convex lens of focal length 20 cm. Draw a ray diagram to find the position and size of the image formed. Mark the optic centre O and the principal focus F on the diagram. Also find the approximate ratio of the size of the image to the size of the object.

Explanation

`{:("Convex lens","Object","image"),(f=+20 cm,h=+4 cm,h.=?),(r=2f=+40cm,u=-30 cm,v=?),(m=?,,):}`
Object is placed between F and `2F_(1)`
The ray diagram is drawn using appropriate scale of measurement.

`OF_(1)=OF_(2)=20 cm " " OC_(1)=OC_(2)=40 cm`
`OB = 30 cm " " AB=4cm`
`B.A.=8 cm`
Ratio of the size of the image to the size of the object.
Magnification `(m)=(v)/(u)=(h.)/(h)=((+60))/((-30))=-2`
Verification :
Using Lens formula `=(l)/(v)-(l)/(u)=(l)/(f)`
`(l)/(v)-(1)/((-30))=(1)/((20)), (l)/(v)=(1)/(20)-(1)/(30),(l)/(v)=(1)/(60), v=+60 cm`
• The image is formed at a distance of 60 cm on the right side of the convex lens. (+ve sign signifies this)
Magnification `(m)=(v)/(u)=(h.)/(h)`
`=((+60))/((-30))=(h.)/(4), -2=(h.)/(4), " " h.=-8cm`
• The image formed (h.) has a height of 8 cm which is more than object height (h). The image formed is enlarged.
• h. has a - ve sign which indicates that the image formed is real and inverted.