Question

An object is placed 25 cm in front of the convex lens whose focal length is 10 cm. (a) Find the image distance and where it is located Now a concave lens is placed 6 cm behind the convex lens and a new image is formed 20 cm behind the convex lens. Draw a rough diagram and indicate the length measurements (b) Calculate the focal length of the concave lens (hint: the image formed by the convex lens will be the object to the concave lens)

Answer 1

 Object distance - $d=25cm$ , Focal length - $F=10cm$

a) from lens formula for convex $\large\frac{1}{d} + \large\frac{1}{f} =\frac{1}{F} \to f = \frac{dF}{d-F} = \frac{25*10}{25-10}=\frac{50}{3}=$ $16.66cm$

it is located right side of the convex lens

b) $d = 20cm -6cm =14cm$ $f = \large\frac{50}{3}-6 = \frac{32}{3}$

from lens formula for concave $\large\frac{1}{d} - \large\frac{1}{f}=-\frac{1}{F}\to F = \frac{df}{d-f}= \frac{3*14*32}{3(42-32)}=$ $44.8cm$