Help with Optics Doubt: Sign Conventions in Problems

[Nikhil_kumar]

.Please provide me with some help in optics. This doubt is in relation to the use of sign conventions in optics. Whenever we prove anything in optics, say for example, when we prove the mirror formula or the lens formula or the lens-maker's formula, we apply the sign conventions in the derivation of the proof itself (u=-ve, f=+ve or -ve etc., according to the New Cartesian Conventions). Then while solving problems based on these formulae, why do we again have to apply the sign conventions according to the data given in the question? I mean, to solve problems based on the lens formula , the mirror formula etc. why do we have to apply the conventions twice? After all the conventions have already been applied during the course of proof itself.

For eg, The lens formula: 1/f=1/v - 1/u is derived in case of real image by convex lens by putting u=-ve, f=+ve v=+ve during the course of proof itself.

 

[Nate810]

Now while solving a problem based on this formula, why do we again have to apply the sign conventions according to the data given in the question? The sign conventions used in the proof of the lens formula are used to denote the positions of the object and image from the lens. That is, it is used to describe the geometry of the particular situation being considered. When solving problems based on the lens formula, the data given in the problem might include a different geometry than the one used in the proof of the lens formula. Therefore, the sign conventions must be applied according to the data given in the problem in order to correctly determine the positions of the object and image relative to the lens.

 

[ogb p]

But while solving problems based on this formula, we again have to put the signs according to the data given in the question.

First of all, it is important to understand that sign conventions in optics are used to represent the direction and nature of light rays. These conventions are based on the direction of the light rays and are used to simplify calculations and understand the behavior of light in different optical systems.

In the derivation of formulas in optics, we use these sign conventions to represent the direction and nature of light rays passing through the optical system. However, when we are solving problems based on these formulas, we need to consider the actual values of the distances and focal lengths involved, which may not always follow the same sign conventions used in the derivation.

For example, in the lens formula, the sign convention for u is negative for real objects, but in a problem, the distance of the object may be positive. In such cases, we need to apply the sign conventions again to ensure that the values we are using in the formula are consistent with the given data.

Moreover, different optical systems may have different sign conventions, and it is important to consider the specific sign conventions for each system while solving problems. This is why we may need to apply the sign conventions multiple times in different problems.

In conclusion, the sign conventions in optics are used to represent the direction and nature of light rays, and they are applied in the derivation of formulas. However, while solving problems, we need to consider the actual values of the distances and focal lengths involved, which may not always follow the same sign conventions used in the derivation. Therefore, it is necessary to apply the sign conventions again to ensure consistency and accuracy in our calculations.