Compound microscope: 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?

Question

Quizplus · Accepted Answer

The magnification of the objective lens is given by $M = \frac{v}{u}$, where $v$ is the image distance and $u$ is the object distance from the lens. Given $M = 30$, we can rearrange the lens formula $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ to solve for $u$, knowing $f = 4.00$ mm and $M = \frac{v}{u} = 30$. Since $v = M \cdot u$, substituting $v = 30u$ into the lens formula gives $\frac{1}{4} = \frac{1}{30u} + \frac{1}{u}$. Solving for $u$ gives approximately $0.13$ mm.

Compound Microscope: the Objective and the Eyepiece of a Microscope