Question

(ii) What is the meaning of magnification produced by a lens? An object of length 5 cm is at a distance of 15 cm from a convex lens. Focal length of the lens is 10 cm. What will be the size of the image?

Answer 1

Meaning of magnification produced by a lens:
The magnification produced by a lens is the ratio of the height of the image to the height of the object. It is also the ratio of the image distance to the object distance. For a lens, the magnification is given by the formula: \[ m = \frac{\text{Image height}}{\text{Object height}} = \frac{v}{u} \] Where \( m \) is the magnification, \( v \) is the image distance, and \( u \) is the object distance.
Now, for the given problem: - Object height \( h_o = 5 \, \text{cm} \)
- Object distance \( u = -15 \, \text{cm} \) (since the object is placed on the left side of the lens, the distance is negative)
- Focal length \( f = 10 \, \text{cm} \)
Using the lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Substituting the given values: \[ \frac{1}{10} = \frac{1}{v} - \frac{1}{-15} \] Simplifying this: \[ \frac{1}{10} = \frac{1}{v} + \frac{1}{15} \] \[ \frac{1}{v} = \frac{1}{10} - \frac{1}{15} \] \[ \frac{1}{v} = \frac{3 - 2}{30} = \frac{1}{30} \] Thus, \[ v = 30 \, \text{cm} \] The magnification \( m \) is then: \[ m = \frac{v}{u} = \frac{30}{-15} = -2 \] Since the magnification is \( -2 \), the image formed is real, inverted, and twice the size of the object. Size of the image: \[ \text{Image height} = m \times \text{Object height} = -2 \times 5 = -10 \, \text{cm} \] Thus, the size of the image is 10 cm, inverted.
% Topic - Optics: Magnification and Image Formation by a Convex Lens \vspace{0.5cm} \hrule \vspace{0.5cm} 2.