Question

Refer to the mirror formula, $\dfrac {1} {v} + \dfrac{1}{u} = \dfrac{1}{f}$, where the symbols have their usual meanings. The nature of graph between u and v is:

Answer 1

Hint: Ray diagrams can be used when positioned at a given position in front of a concave mirror to determine the image location, height, orientation and shape of image created by objects. Ray diagrams offer valuable knowledge about interactions between objects and images, but do not provide the details in a quantitative manner.

Complete step by step solution:
Mirror equation is an equation relating object distance and image distance with focal length is known as a mirror equation. It is also known as a mirror formula.
In a spherical mirror, the distance between the object and the mirror pole is called the distance of the object ($u$), the distance between the image and the mirror pole is called the distance of the image ($v$), the distance between the main focus and the mirror pole is called the focal length ($f$).

The object distance, image distance, and focal length are linked in ray optics as,
$\dfrac {1} {v} + \dfrac{1}{u} = \dfrac{1}{f}$
The above formula is true for all forms of spherical mirrors (Concave and Convex) and for all object positions in all circumstances.
The mirror formula can be written as,
\[\dfrac{1}{u} = \dfrac {{- 1}} {v} + \dfrac{1}{f}\]
Comparing the equation with $y = mx + c$, the slope of the graph will be $ - 1$ and intercept will be $\dfrac {1} {f} $.

The graph will be a straight line between $1/v$ and $1/u$ and the graph between $v$ and $u$ will be hyperbola.

To prevent uncertainty in the interpretation of the ray paths, the Current Cartesian Sign Convention is used. For simple visualisation, refer to the diagram. The optical core of the lens is considered for measuring all the distances.

Note: While a ray diagram may assist one to determine the image's approximate location and size, numerical information about image distance and object size will not be provided. The Mirror Equation and the Magnification Equation should be used to obtain this kind of numerical knowledge.