E14. The objective lens of a microscope has a focal length of 0.6 cm . An object on the microscope slide is placed at a distance of 0.9 cm from the lens. a. At what distance from the lens is the image formed by the objective lens? b. What is the magnification of this image?

Let's solve the problem step by step using the thin lens formula and the magnification formula. ### Given: - **Focal length of the objective lens (f):** 0.6 cm - **Object distance (u):** 0.9 cm ### a. **Finding the Image Distance (v)** The **thin lens formula** is given by: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] Rearranging to solve for \( v \): \[ \frac{1}{v} = \frac{1}{f} - \frac{1}{u} \] Substitute the given values: \[ \frac{1}{v} = \frac{1}{0.6\ \text{cm}} - \frac{1}{0.9\ \text{cm}} = \frac{5}{3} - \frac{10}{9} = \frac{15}{9} - \frac{10}{9} = \frac{5}{9} \] \[ v = \frac{9}{5} = 1.8\ \text{cm} \] **Image Distance, \( v = 1.8\ \text{cm} \)** ### b. **Calculating the Magnification (m)** The **magnification formula** is: \[ m = \frac{v}{u} \] Substitute the known values: \[ m = \frac{1.8\ \text{cm}}{0.9\ \text{cm}} = 2 \] **Magnification, \( m = 2 \) (or \( 2 \times \))** ### **Summary:** - **a.** The image is formed **1.8 cm** from the lens. - **b.** The magnification of the image is **2×**.