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.

An object of height 4 cm is placed at a distance of 30 cm from the opt

1.	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.
Answer» SOLUTION :`{:("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.