Question

The microscope available in your biology lab has a converging lens (the eyepiece) with a focal length of 2.50 cm mounted on one end of a tube of adjustable length. At the other end is another converging lens (the objective) that has a focal length of 1.00 cm. When you place the sample to be examined at a distance of 1.30 cm from the objective, at what length will you need to adjust the tube of the microscope in order to view the sample in focus with a completely relaxed eye?

Note that to view the sample with a completely relaxed eye, the eyepiece must form its image at infinity.

Answer 1

Concepts and reason

The concepts used to solve this problem are convex lens and thin lens equation .

In a two-lens system, the image formed by one lens acts as an object for the other lens.

First, find the expression for the image distance formed by the objective.

Then, Consider this image as a object for the eyepiece and find the expression for the distance from the eyepiece.

Finally, sum the image distance of the objective and object distance of the eyepice, and calculate the length needeed to adjust the tube of the microscope.

Fundamentals

Converging lens focus a beam of parallel light into the small region at a focal point.

The expression for thin lens equation is,

Here, is the object distance for objective, is the image distance for the objective, and is the focal length of the objective.

The expression for thin lens equation is,

Rearrange the above expression,

When the eyepiece is to form an image at infinity, the object for the eyepiece should be located at the focal point of the eyepiece.

So,

Here, is the object distance of eyepiece and is the focal length of the eyepiece.

The image viewed by the observer is an image of an image.

The length needed to adjust the tube of the microscope is represented by .

The length of the tube is then the sum of the image distance for the objective and object distance for the eyepiece.

$p+p=1 $

Substitute for and for .

Substitute for , for , and for .

Ans:

The length needed to adjust the tube of the microscope is .

Answer 2

fob= 1 cm
dob = 1.3 cm
fep = 2.5 cm

dib = dob * fob/dob -fob = 1.3 * 1/1.3 - 1 = 4.33 cm

Length of the tube :
x = dib + dep ---->to view the sample in focus with a completely relaxed eye : dep =fep = 2.5 cm



--> X = 4.33 + 2.5 = 6.83 cm

Answer 3

Use the following lens equation For the objective, 1.0 cm 1.3 cm q q 4.33 cm In a microscope, the image from the objective forms at the focal point of the eyepiece. Therefore, the distance between the objectiveand the eyepiece. dq+J. -4.33 cm+2.5 cm -6.83 cm 40,