A 5 mm high pin placed at a distance of 15 cm from convex lens of focal length 10 cm. A second lens of focal length 5 cm is placed 40 cm from the first lens and 55 cm from the pin. Find (a) the position of the final image, (b) its nature and (c) its size.

focal length of first convex lens, = 10cm

focal length of second convex lens, = 5 cm

length of the pin(height)= 5 mm

distance between the first lens and pin= 15 cm

distance between the second lens and pin= 55 cm

(a) image formed by the first lens

Distance of object from lens, u= -15cm

By using lens formula,

Now, this image will act as an object for next lens, hence, object distance foe second lens is

By using lens formula,

Therefore, the image formed will be 10cn to the right of second lens.

(b) magnification by first lens, m is given by

magnification by second lens, m is given by

Hence, the image formed is erect and real.

(c) size of the final image is 10mm