The objective and the eyepiece of a microscope have focal lengths of 4.00 mm and 25.0 mm,respectively.The objective produces a real image 30 times the size of the object.The final image is viewed at infinity,and the near point of the microscope user is at 25.0 cm.What is the distance between the object and the focal point of the objective?
A) 0.13 mm
B) 0.18 mm
C) 0.23 mm
D) 0.28 mm
E) 0.33 mm

Question

Quizplus · Accepted Answer

The magnification produced by the objective lens is given by $M = \frac{v}{u}$, where $v$ is the image distance (from the lens to the image) and $u$ is the object distance (from the lens to the object). Given that the magnification is 30, we have $30 = \frac{v}{u}$. The lens equation is $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$, where $f$ is the focal length of the lens. Substituting $v = 30u$ into the lens equation and the given focal length of 4.00 mm, we get $\frac{1}{4} = \frac{1}{30u} + \frac{1}{u}$. Solving for $u$, we find that $u$ is approximately 0.13 mm.

The Objective and the Eyepiece of a Microscope Have Focal