Question

If the magnification is less than 1 is the image real and inverted or is it virtual and erect? Also can someone write me the table of sign conventions for both the mirrors and lenses??

Answer 1

In most cases the height of the image differs from the height of the object, meaning that the mirror has done some magnifying (or reducing). The magnification, m, is defined as the ratio of the image height to the object height, which is closely related to the ratio of the image distance to the object distance:

A magnification of 1 (plus or minus) means that the image is the same size as the object. If m has a magnitude greater than 1 the image is larger than the object, and an m with a magnitude less than 1 means the image is smaller than the object. If the magnification is positive, the image is upright compared to the object; if m is negative, the image is inverted compared to the object.

Answer 2

• If the magnification is less than 1 then the image formed is inverted and real as size of image is smaller than size of object.
• This image is formed when object is placed between optical centre and focus of curvature of lens or mirror.

Sign convention for mirror:--

1. All ray diagrams are drawn with the incident light travelling from left to right.
2. All distances are measured from the pole of the mirror.
3. All distances measured in direction of incident ray are taken to be positive.
4. All distances measured in opposite direction of incident light are taken to be negative.
5. Heights measured in upwards and perpendicular to principle axis are taken positive.
6. Heights measured downwards and perpendicular to axis are taken negative.
7. According to sign convention focal length and radius of curvature are negative for concave mirror and positive for convex mirror.

Sign convection for lens:--

1. All distances are measured from optical centre of the lens.
2. All distances measured in direction of incident ray are taken to be positive.
3. All distances measured in opposite direction of incident light are taken to be negative.
4. Heights measured in upwards and perpendicular to principle axis are taken positive.
5. Heights measured downwards and perpendicular to axis are taken negative.
6. Focal length of converging lens (convex lens)  is positive and that of diverging lens (concave lens) is negative.