Question

Ade school student plans to build a 30-power telescope as a science fair project. She starts with a magnifying glass with a focal length of 8.5 cm as the eyepiece. What focal length is needed for her objective lens?

Answer 1

The student will need an objective lens with a focal length of approximately -3.93 mm for their 30-power telescope.

Step-by-step explanation:

To calculate the focal length of the objective lens for a 30-power telescope, we can use the formula:

Power of telescope = Power of objective lens x Power of eyepiece lens

Since the magnifying glass has a focal length of 8.5 cm, it has a power of 1/focal length = 1/8.5 = 0.118. The eyepiece lens will have a power of -30 (since it is the eyepiece of a telescope with 30-power magnification).

Using the formula: 0.118 x Power of objective lens = -30, we can solve for the objective lens power:

Power of objective lens = -30 / 0.118 = -254.24

Since power (P) is equal to 1/focal length (f), we can rearrange the formula to solve for the focal length:

Focal length of objective lens = 1 / Power of objective lens = 1 / -254.24 = -0.00393 meters, or approximately -3.93 mm

Therefore, the focal length needed for the objective lens is approximately -3.93 mm.