Question

Two convex lenses A and B, each of focal length 10.0 cm, are mounted on an optical bench at 50.0 cm and 70.0 cm respectively. An object is mounted at 20.0 cm. Find the nature and position of the final image formed by the combination.

Hint:

To solve combined lens problems, first find the image formed by the first lens and use this as the object for the second lens.

Answer 1

Step 1: Finding the image formed by the first lens . For lens A, the object distance is \( u_1 = -20.0 \, \text{cm} \) (since the object is real) and the focal length is \( f_1 = 10.0 \, \text{cm} \). Using the lens formula: \[ \frac{1}{f_1} = \frac{1}{v_1} - \frac{1}{u_1} \] \[ \frac{1}{10.0} = \frac{1}{v_1} - \frac{1}{-20.0} \] \[ v_1 = 20.0 \, \text{cm} \] So, the image formed by lens A is at \( v_1 = 20.0 \, \text{cm} \), which is real and inverted. 

Step 2: Finding the image formed by the second lens . The image formed by lens A acts as the object for lens B. The object distance for lens B is the distance between the two lenses, i.e., \( u_2 = 70.0 - 20.0 = 50.0 \, \text{cm} \). Using the lens formula for lens B: \[ \frac{1}{f_2} = \frac{1}{v_2} - \frac{1}{u_2} \] \[ \frac{1}{10.0} = \frac{1}{v_2} - \frac{1}{50.0} \] \[ v_2 = 12.5 \, \text{cm} \] Thus, the final image is formed at a distance of 12.5 cm from lens B, which is real and inverted.