A microscope has an objective lens of focal length 1.40 mm and an eyepiece of focal length 20.00 mm.It is adjusted for minimum eyestrain for persons with a near point of 25.0 cm.A blood sample is placed 1.50 mm from the objective.How far apart are the lenses?
A)20 mm
B)21 mm
C)23 mm
D)41 mm

Question

Quizplus · Accepted Answer

For minimum eyestrain, the image formed by the objective lens acts as the object for the eyepiece and is at the near point of the observer, which is 25.0 cm (250 mm) from the eyepiece. The objective lens forms its image at a distance $d_i$ given by the lens equation $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$, where $f$ is the focal length of the objective lens and $d_o$ is the object distance from the objective lens. For the objective lens, $f = 1.40$ mm and $d_o = 1.50$ mm, so we find $d_i$. For the eyepiece to form an image at the near point, we use its focal length $f = 20.00$ mm and the image distance $d_i' = -250$ mm (negative because the image is virtual and on the same side of the lens as the object). We then find the object distance for the eyepiece $d_o'$ and add it to $d_i$ to get the total distance between the lenses.Objective lens:$\frac{1}{1.40} = \frac{1}{1.50} + \frac{1}{d_i}$Solving for $d_i$ gives $d_i = 42$ mm.Eyepiece:$\frac{1}{20} = \frac{1}{d_o'} - \frac{1}{250}$Solving for $d_o'$ gives $d_o' = -22.22$ mm (negative indicates the direction relative to the lens).The total distance between the lenses is the sum of $|d_i|$ for the objective and $|d_o'|$ for the eyepiece, which is $42 + 22.22 = 64.22$ mm. However, this calculation seems to have an error in interpreting the setup for the eyepiece calculation and the total distance calculation, leading to a misunderstanding in the final answer.The correct approach involves understanding that when adjusted for minimum eyestrain, the final image is at infinity, and the intermediate image (formed by the objective) is located at the focal point of the eyepiece. Thus, the distance between the lenses is the sum of the image distance from the objective and the focal length of the eyepiece.Correcting the explanation: The image distance $d_i$ from the objective lens is found using the lens formula, considering the object distance $d_o = 1.50$ mm and the focal length $f = 1.40$ mm. The image formed by the objective lens serves as the object for the eyepiece, and for minimum eyestrain, this image is at the focal point of the eyepiece. Therefore, the distance between the lenses is the sum of the image distance from the objective lens and the focal length of the eyepiece. The calculation error in the initial explanation led to an incorrect interpretation of how the distances should be summed and the role of the eyepiece in forming the final image for minimum eyestrain.

A Microscope Has an Objective Lens of Focal Length 1