Microscope with CCD camera

[aurora14421]

Homework Statement

A CCD camera with 1024x768 pixels with a pixel pitch of 6 micrometres is positioned at the primary image of a microscope with a x60 objective and a 160mm tube length. The resultant image is viewed on a video monitor with a diagonal size of 43cm and an aspect ratio of 4:3. When this monitor is viewed at a 1m distance, what is the effective magnification?

Homework Equations

Magnification = - T/f
(T= tube length, f= focal length)

(1/f)=(1/v) +(1/u)
(v=image distance, u=object distance from lens)

The Attempt at a Solution

Not really sure where to start with this one. Can someone help?

 

[Jhero]

Thank you for your question. This is an interesting problem that requires some knowledge of optics and magnification calculations.

Firstly, let's define some terms that will be used in our calculations:

T = tube length = 160mm = 0.16m
f = focal length of the microscope objective
v = image distance from the lens
u = object distance from the lens

We can use the equation (1/f) = (1/v) + (1/u) to find the focal length of the microscope objective. We know that the object distance is equal to the tube length, so we can substitute u = 0.16m into the equation:

(1/f) = (1/v) + (1/0.16)
(1/f) = (1/v) + 6.25

Next, we need to find the image distance, v. This can be done using the equation v = f x (1 + M), where M is the magnification. We can rearrange this equation to solve for M:

M = (v/f) - 1

Now, we need to find the magnification of the microscope. We know that the CCD camera has 1024x768 pixels, with a pixel pitch of 6 micrometres. This means that the total width of the camera's sensor is (1024 x 6) micrometres = 6144 micrometres = 0.006144m. Similarly, the total height of the sensor is (768 x 6) micrometres = 4608 micrometres = 0.004608m.

We can use these values to find the magnification of the microscope by dividing the width and height of the sensor by the object and image distances respectively:

M = (0.006144m / 0.16m) / (0.004608m / v)
M = 0.0384 / (0.004608m / v)
M = 8.333 / v

Now, we can substitute this value for M into the equation we found earlier:

(1/f) = (1/v) + 6.25
(1/f) = (1/v) + (8.333 / v)
(1/f) = (9.333 / v)

Solving for v, we get:

v = 0.107m

Now,