See according to the New Cartesian Sign convention U i.e., the object distance is always in the left hand side of the lens or mirror i.e., to -X side. That is why U is always taken as negative. For focal length, f in lens is always taken as negative for concave and positive for convex. In case of mirror the f is taken as negative if it is in -X side i.e., is in Concave mirror and taken as positive if it is in +X side i.e., is in Convex mirror. And for image distance, V in lens it is taken as positive in Convex lens since image is formed on +X side. It is taken as negative in Concave lens since image is formed in -X side of the Cartesian. In Concave mirror V is taken as positive and negative for convex mirror.

Depth offield vsdepth of focus microscope

Is okay but when solving problem sums sometimes $v$ becomes negative sometimes $u$ and many times $f$. Sometimes both $v$ and $f$ becomes negative. I just can't mug up why this is happening.

Depth of focus microscopeexample

Now the convex lens converges the incident rays. Hence the rays converge to a single point infront of the lens. So the image distance is positive here.

you can easily verify that the focal length is in the positive x direction for a convex lens while it is along the negative x direction for a concave lens. So f is positive for a convex lens and negative for a concave lens. The reason is the sign altering of v.

Depth offieldmicroscopeformula

This convention means $u$ is normally negative because the object is to the left of the lens, while $v$ is normally positive because a (real) image is to the right of the lens. The lens equation becomes:

Depth of focusin optics

I have a great deal of sympathy with your position. As taught in schools the sign convention is somewhat vague and that gets confusing with complicated setups.

Depth of focus microscopepdf

Just think in terms of their properties. A concave lens diverges the rays incident on it. So the image will be formed behind the lens. So the image distance becomes negative. (The image distance is measured from the principal point to the point at which the image is formed.)

By the depth of field of the microscope we mean the thickness of the layer of the preparation in which the sharply displayed objects are located. The depth or thickness of such a layer of the object indicates the depth of field, or depth of field (penetration ability i.e. "ability to draw sharply in depth") of the lens. Objects that lie above and below this layer are seen out of focus or are not visible at all.

The depth of field depends inversely on the numerical aperture of the lens, i.e. for a strong lens the depth of field is quite small.

Depth of focusformula

If you're dealing with anything complicated I recommend keeping strictly to the Cartesian sign convention. I've linked an article that seems to be a good summary of this, but Googling will find you lots more articles to look at. Basically:

Depth of focusdefinition

Lenses with lower magnification (eg 4x, 10x) have a greater depth of field than lenses with higher magnification (eg 40x, 60x, 100x). Depth of field can be increased by zooming in or lowering the position of the condenser. Thus, details and impurities lying above and below the object can be displayed. On the contrary, we achieve a decrease in the depth of field as the aperture of the lens increases.

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Basically everything to the left and down is negative, everything to the right and up is positive. Curvatures are measured from the vertex to the center of the curvature.

When viewing the transparent preparation, we make a cut through the preparation, we can clearly observe only a thin layer. We are talking about„the optical section“. The microscope will clearly show us the structures that lie in it. So focusing is actually just the localization of object structures, or the entire observed object into this layer. By turning the micrometric screw, which allows us to focus on the given object, we pass a series of consecutive optical sections through the observed object.