What is lens formula?Give its sign conventions and assumptions.
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I).Lens Formula: A formula which gives the relationship between image distance, object distance and focal length of lens is known as focal length.
1/f=1v-1/u
where f=focal length, u=object distance and v=image distance.
ii)Sign Conventions for spherical Lenses:
According to new Cartesian sign convention, object is always placed on the left side of the lens
1. All the distance are measured from optical centre (c) of lens to the right side will be considered positive because they will be in the same direction of incident ray
2. On the other hand, distance measured from optical centre to the left side are considered as negative.
3. Focal length of convex lens is positive and concave lens is negative.
4. The distances measured upward and perpendicular to the principal axis are taken as positive.
5. The distance measured downward and perpendicular to the principal axis is considered negative.
III) Rules for obtaining images formed by convex lens:
1. A ray of light which is parallel to the principal axis of lens , passes through focus after refraction through lens.
2. A ray of light passing trough the optical center of convex lens goes straight after refraction trough lens.
3. A ray of light passing through the focus of a convex lens becomes parallel to principal axis after refraction through lens
1/f=1v-1/u
where f=focal length, u=object distance and v=image distance.
ii)Sign Conventions for spherical Lenses:
According to new Cartesian sign convention, object is always placed on the left side of the lens
1. All the distance are measured from optical centre (c) of lens to the right side will be considered positive because they will be in the same direction of incident ray
2. On the other hand, distance measured from optical centre to the left side are considered as negative.
3. Focal length of convex lens is positive and concave lens is negative.
4. The distances measured upward and perpendicular to the principal axis are taken as positive.
5. The distance measured downward and perpendicular to the principal axis is considered negative.
III) Rules for obtaining images formed by convex lens:
1. A ray of light which is parallel to the principal axis of lens , passes through focus after refraction through lens.
2. A ray of light passing trough the optical center of convex lens goes straight after refraction trough lens.
3. A ray of light passing through the focus of a convex lens becomes parallel to principal axis after refraction through lens
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Note :
- f = focal length
- v = distance of image .
- u = distance of object .
Lens formula :
1 / f = 1 / v - 1 / u
Concave lens :
f = negative
u = negative
v = negative
Convex lens
f = positive
u = negative
v = positive for real image ,
v = negative for virtual image .
The optical centre is chosen as the origin of the coordinate system.
With respect to optical centre :
The part which are above are positive, below negative.
The part which are right are positive while left is negative.
This is just like the normal x-axis and y-axis in the co-ordinate system .
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