Question

The position of the image formed by the combination of lenses is :

• A. 30 cm (right of third lens)
• B. 15 cm (left of second lens)
• C. 30 cm (left of third lens)
• D. 15 cm (right of second lens)

Answer 1

Answer: (A)

30 cm (right of third lens)

Answer 2

The image positions are calculated lens by lens using the lens formula:
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u} \implies v = \frac{uf}{u + f}.$
For lens 1 ($f_1 = 10 \, \text{cm}, u = -30 \, \text{cm}$):
$v = \frac{(-30) \times 10}{-30 + 10} = \frac{-300}{-20} = 15 \, \text{cm}.$
The image forms 15 cm to the right of the first lens.
For lens 2 ($f_2 = -10 \, \text{cm}, u = 10 \, \text{cm}$):
$v = \frac{10 \times (-10)}{10 - 10} = \infty.$
The image is formed at infinity due to parallel rays after the second lens.
For lens 3 ($f_3 = 30 \, \text{cm}, u = -\infty$):
$v = f_3 = 30 \, \text{cm}.$
Thus, the final image is formed 30 cm to the right of the third lens.