Name: Telescope
Uploaded: 2019-07-19
Duration: 7 min 39 s
Description: How do you see the details of distant objects? Do you want to learn an amazing optical instrument used to see distant objects' details? Watch this video.

Question

Explain about the compound microscope and obtain the equation for magnification

Accepted Answer

A compound microscope is an optical instrument consisting of two convex lenses of short focal lengths which is used for observing the highly magnified images of tiny objects.

It consists of two lenses. A lens of short aperture and short focal length facing the object is called the object lens and another lens of short focal length but large aperture is called the eye lens. The two lenses are placed coaxially at the two ends of a tube. To focus over an object, the distance of the object lens from the object is adjusted with the help of rack and pinion arrangement.
Working: When a small object is placed just outside the focus ( $f_{o}$ ) of the object lens, its real, inverted and magnified image is produced on the other side of the lens beyond $f_{o_{}}$ The image produced by the object lens acts as object for the eye lens. The distance of the object from the object lens is so adjusted that the final image is formed at the least distance of distinct vision from the eye.

The magnifying power of the microscope is defined as the ratio of the angle subtended by the final image to that subtended by the object at the eye, when both are situated at the least distance of clear vision.

$m = \frac{β}{α} = \frac{tanβ}{tanα} = \frac{\frac{A'' B''}{A'' C'}}{\frac{A'' Q}{A' C'}} = \frac{A'' B''}{A' Q} = \frac{A'' B''}{AB} = \frac{A'' B''}{A'' B} \times \frac{A' B'}{A B} = m_{o} \times m_{e}$

where $m_{0,} m_{e}$ =are the magnification produced by the objective and the eye piece respectively. As

As the eye piece is working as a simple microscope, we have

$m_{e} = (1 + \frac{d}{f_{e}})$ and $m_{o} = \frac{A' B'}{AB} = \frac{v_{o}}{- u_{o}}$ , therefore we can write,

$m = \frac{v_{o}}{u_{o}} \{1 + \frac{d}{f}\}$

If the object is very close to the focus of the objective and, and the $A' B'$ is very close to the eye lens, whose focal length is also small $v_{0} = CC' =$ ,length of the microscope ,

$m = \frac{L}{- f_{o}} \{1 + \frac{d}{f_{e}}\},$

As $\frac{1}{v_{o}} - \frac{1}{u_{o}} = \frac{1}{f_{o}} or \frac{v_{o}}{u_{o}} = \{1 - \frac{v_{}}{f_{o}}\}$ , therefore

$m = (1 - \frac{v_{o}}{f_{o}}) (1 + \frac{d}{f_{e}})$

Explain about the compound microscope and obtain the equation for magnification

Important Questions on Optical Instruments

Learn and Prepare for any exam you want !