Explain about compound mircoscope and obtain the equation for magnification. Compound microscope:

Explanation

The lens near the object, called the objective, forms a real, magnified image of the object. This serves as the object for the second lens which is the eyepiece. Eyepiece serves as a simple microscope that produce finally an enlarged and virtual image. The first inverted image formed by the objective is to be adjusted close to, but within the focal plane of the eyepiece so that the final image is formed nearly at infinity or at the near point. The final image is inverted with respect to the original. We can obtain the magnificaiton for a compound microscope.
Magnification of compound microscope
From the ray diagram, the linear magnification due to the objective is,
`m_(0) = (h.)/(v)`
From the figure, `tan beta = (h)/(f_(0)) = (h.)/(L.)` then
`(h.)/(h)=(L)/(f_(0)),m_(0)=(L)/(f_(0))`
Here, the distance L is between the first focal point of the eyepiece to the second focal point of the objective. This is called the tube lenght L of the microscope as `f_(0) and f_(e)` are comparatively smaller than L. If the final image is formed at p (near point focusing), the magnification `m_(e)` of the eyepiece is,
`m_(e) = 1 + (D)/(f_(e))`
The total magnification m in near point focusing is,
`m=m_(o)m_(e)=((L)/(f_(o)))(1+(D)/(f_(e)))`
If the image is formed at infinty (normal focusing), the magnificaiton `m_(e)` of the eyepiece is,
`m_(e) = (D)/(f_(e))`
The total magnification m in normal focusing is,
`m=m_(o)m_(e)=((L)/(f_(o)))((D)/(f_(e)))`