Rules of new cartesian sign convention:

(i) The focal length of a convex lens is positive and that of a concave lens is negative.

(ii) Object distance u is always negative as it is on the left side of the mirror.

(iii) The distance of real image is positive and that of virtual image is negative.

(iv) The height of the object h is always positive. Height h’, of virtual and erect image is positive and that of real and inverted image is negative.

(v) The linear magnification, m = h’/h is positive for a virtual image and negative for a real image.

New cartesian sign convention for refraction of light through spherical lenses. According to this sign convention:

(i) All distances are measured from the optical centre of the lens.

(ii) The distances measured in the same direction as the incident light are taken positive.

(iii) The distances measured in the direction opposite to the direction of incident light are taken negative.

(iv) Heights measured upwards and perpendicular to the principal axis are taken positive.

(v) Heights measured downwards and perpendicular to the principal axis are taken negative.

Fig. New cartesian sign convention for a lens

Given,

Refractive index of the liquid, = 1.3

Apparent depth of the object = 7.7 cm

Refractive index =

Therefore,

Convex lens |
Concave lens |

1. It is thicker at the centre than at the edges. |
1. It is thinner at the centre than at the edges. |

2. It converges a parallel beam of light after refraction through it. |
2. It diverges a parallel beam of light on refraction through it. |

3. It has a real focus. |
3. It has a virtual focus. |