Question

An object is placed at a distance of X from a convex lens, when a real image is formed at a distance of 15 cm from the lens. If the focal length of the lens is 10 cm, calculate (a) value of X (b) the magnification produced. State the characteristics of the image.

Answer 1

(a) Distance of the object from the lens (u) = X

Distance of the image from the lens \((v)=+15 \mathrm{~cm} \quad\{\because\) Image is real \(\}\)

Focal length of the convex lens \((f)=+10 \mathrm{~cm} \quad\{\because\) Lens is convex \(\}\)

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

\[ \Rightarrow \ \frac{1}{15} - \frac{1}{\mathrm{X}} = \frac{1}{10}, \qquad \Rightarrow \ -\frac{1}{\mathrm{X}} = \frac{1}{10} - \frac{1}{15} \]

\[ \Rightarrow \ -\frac{1}{\mathrm{X}} = \frac{3 - 2}{30}, \qquad \Rightarrow \ -\frac{1}{\mathrm{X}} = \frac{1}{30} \]

\[ \therefore \ \mathrm{X} = - \ 30 \ \text{cm} \]

Thus, the object is at a distance of 30 cm from the convex lens. The minus sign shows that the distance of the object is measured opposite the direction of the incident light.

(b) (i) Magnification : \[ m = \frac{v}{u} = \frac{15}{30} = 0.5. \]

(ii) The image is real, inverted and diminished.