Question

You have two converging lenses with focal lengths of 4.5 cm and 2.0 cm At what distance must the lenses be positioned to act as a microscope with M = 50⁹ Express your answer with the appropriate units. ?

Answer 1

To calculate the position of the lenses to act as a microscope with a given magnification, use the formula M = -(d/f_1)(f_2/(f_1+f_2)). Plugging in the values, the lenses must be positioned approximately 528,800,000 cm apart to act as a microscope with a magnification of 50⁹.

Step-by-step explanation:

To calculate the position of the lenses to act as a microscope with a given magnification, we can use the formula:

M = -(d/f_1)(f_2/(f_1+f_2))

Here, d is the total distance between the lenses, f_1 is the focal length of the first lens, f_2 is the focal length of the second lens, and M is the magnification.

Using the given values, we have M = 50⁹ and f_1 = 4.5 cm and f_2 = 2.0 cm. Plugging these values into the formula, we can solve for d.

d = -M(f_1+f_2)/(f_2/f_1)

Substituting the values, d = -(50⁹)(4.5 cm + 2.0 cm)/(2.0 cm/4.5 cm)

d = -50⁹(6.5 cm)/(0.444444)

d ≈ 5.288 × 10⁷ cm or 528,800,000 cm

Therefore, the lenses must be positioned approximately 528,800,000 cm apart to act as a microscope with the given magnification.