Lens Formula Confusion: Convex Lens, Cartesian Sign Conv.

[anigeo]

The cartesian sign convention for a convex lens is follows:
1. All distances on the principal axis are measured from the optical center.
2. The distances measured in the direction of incident rays are positive and all the distances measured in the direction opposite to that of the incident rays are negative.
3. All distances measured above the principal axis are positive. Thus, height of an object and that of an erect image are positive and all distances measured below the principal axis are negative.

Then for a convex lens when the object is placed between 2f and f,the image is formed between pole and f on the other side.
The lens equation is 1/f=1/v-1/u.
In this case,
v,f>0 and u<0.
then 1/u=1/v-1/f=(f-v)/(vb)>0,.....BUT HOW CAN THIS BE TRUE as u<0.

 

[Simon Bridge]

draw the ray diagram and notice that v > f
therefore, f-v < 0
which comes as no surprise because u < 0

what's the problem?

 

[anigeo]

Thanks Simon,i just made a small mistake.

 

[Simon Bridge]

Happen to the best of us ;)

 

[sardar]

Thank you for sharing the cartesian sign convention for a convex lens. It is important to note that this convention is just a mathematical tool for simplifying calculations and does not change the physical properties of the lens. Therefore, it is not necessary for the values of u, v, and f to always follow the cartesian sign convention.

In the case you mentioned, when the object is placed between 2f and f, the image is formed between the pole and f on the other side. This means that v is positive, which follows the cartesian sign convention. However, the value of u is negative, which does not follow the convention. This is because the object is placed on the opposite side of the lens from the incident rays, which is why it is negative.

As for the lens equation, it is a mathematical representation of the relationship between the object distance (u), image distance (v), and focal length (f). The equation does not depend on the sign convention, as it is a general formula that can be used for any type of lens. Therefore, it is not necessary for all the values to follow the cartesian sign convention for the equation to work.

In summary, the cartesian sign convention is a helpful tool for simplifying calculations, but it is not a rule that must always be followed. The values of u, v, and f can vary depending on the specific situation, and the lens equation will still hold true. I hope this helps to clarify any confusion.