Question

A convex lens of focal length 10 cm is placed at a distance of 60 cm from a screen. How far from the lens should be placed an object so as to obtain a real image on the screen? Calculate the magnification of the image and its characteristics.

A convex lens of focal length 10 cm is placed at a distance of 60 cm from screen.

1. How far should an object be placed from the convex lens to obtain a real image on the screen?
2. What is the magnification of image?

Answer 1

\[ \text{(a) Distance of the image from the lens } (v) = + \ 60 \ \text{cm} \qquad \{\because \ \text{Image is real}\} \]

\[ \text{Focal length of the convex lens } (f) = + \ 10 \ \text{cm} \qquad \{\because \ \text{Lens is convex}\} \]

\[ \text{Distance of the object from the lens } (u) = \ ? \]

\[ \text{Applying, } \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]

\[ \Rightarrow \ \frac{1}{60} - \frac{1}{u} = \frac{1}{10}, \qquad \Rightarrow \ -\frac{1}{u} = \frac{1}{10} - \frac{1}{60} \]

\[ \Rightarrow \ -\frac{1}{u} = \frac{6 - 1}{60}, \qquad \Rightarrow \ -\frac{1}{u} = \frac{1}{12} \]

\[ \therefore \ u = - \ 12 \ \text{cm} \]

\[ \text{Thus, the object should be placed at a distance of 12 cm from the convex lens.} \]

\[ \text{(b) (i) Magnification : } m = \frac{v}{u} = \frac{60}{12} = 5. \]

\[ \text{(ii) The image is real, inverted and enlarged.} \]