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Chapter 35: Q. 40 (page 1018)

Mordern microscopes are more likely to use a camera than human viewing. This is accomplished by replacing the eyepiece in figure 35.14with a photo-ocular that focuses the image of the objectives to a real image on the sensor of a digital camera. A typical sensor is 22.5mmwide and consists of 56254.0渭mwide pixels. suppose a microscopist pairs a 40Xobjectives with a 2.5Xphoto-ocular

a. what is the field of view? That is what width on the microscope stage in mmfills the sensor?

b. The photo of a cell is 120pixelsin a diameter. what is the cell's actual diameter in渭m?

Short Answer

Expert verified

a. The field of view is 蝇1=0.225mm.

b. The cell's actual diameter isd=4.8渭m.

Step by step solution

01

Part (a) Step 1: Given information 

We have given that:

Magnification of objectmobj=40,

width of typical sensor蝇s=22.5mmand

magnification of photo ocularM伪=2.5.

We need to find the magnification M .

02

Part (a) Step 2: Simplification 

Let us find Magnification M:

M=mobjM伪 (substitute values in equation.)

M=(40)(2.5)

M=100

Therefore width 蝇1will be,

蝇1=蝇sM

substituting the values we get ,

蝇1=0.225mm

Here,蝇1is the field of view.

03

part (b) Step 1: Given Information 

We need to find the cell's actual diameter in 渭m.

04

part (b) step 2: Simplification

Firstly we have to find width 蝇2of the photo of the cell:

蝇2=120pixel4.0渭m/pixel蝇2=480渭m

Therefore Diameter is:

d=蝇2Md=480渭m100d=4.8渭m. (substituting value in the equation.)

Here, dis the cell's actual diameter.

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Most popular questions from this chapter

A common optical instrument in a laser laboratory is a beam expander. One type of beam expander is shown in FIGURE P35.29.

The parallel ray of a laser beam of width 蝇1enter from the left.

a. For what lens spacing d does a parallel laser beam exit from the right?

b. What is the width 蝇2of the exiting laser beam?

The rays leaving the two-component optical system of FIGUREP35.27produce two distinct images of the1.0cm-tall object. what are the position (relative to the lens), orientation, and height of each image?

What is thef-numberof a lens with a 35mmfocal length and a7.0mmdiameter aperture?

The resolution of a digital camera is limited by two factors:

diffraction by the lens, a limit of any optical system, and the fact

that the sensor is divided into discrete pixels. Consider a typical

point-and-shoot camera that has a 20-mm-focal-length lens and

a sensor with 2.5@mm@wide pixels.

a. First,ass ume an ideal, diffractionless lens. At a distance of

100 m, what is the smallest distance, in cm, between two

point sources of light that the camera can barely resolve? In

answering this question, consider what has to happen on the

sensor to show two image points rather than one. You can use

s鈥� = f because s W f.

b. You can achieve the pixel-limited resolution of part a only if

the diffraction width of each image point is no greater than

1 pixel in diameter. For what lens diameter is the minimum

spot size equal to the width of a pixel? Use 600 nm for the

wavelength of light.

c. What is the f-number of the lens for the diameter you found in

part b? Your answer is a quite realistic value of the f-number

at which a camera transitions from being pixel limited to

being diffraction limited. For f-numbers smaller than this

(larger-diameter apertures), the resolution is limited by the

pixel size and does not change as you change the aperture. For

f-numbers larger than this (smaller-diameter apertures), the

resolution is limited by diffraction, and it gets worse as you

鈥渟top down鈥� to smaller apertures

A narrow beam of white light is incident on a sheet of quartz. The beam disperses in the quartz, with red light (l鈮�400nm)traveling at an angle of 26.3掳with respect to the normal and violet light (l鈮�400nm) traveling at 25.7掳 . The index of refraction of quartz for red light is 1.45. What is the index of refraction of quartz for violet light?
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