Question

derive lens formula and explain magnificatio ​

Answer 1

OA=object distance=u
OA'=image distance=v
Triangle OAB similar to Triangle OA'B'
angleBAO=angle B'A'O=90°
so, angle AOB=angleA'B'O
A'B'/AB=OA'/OA ---------------(1)

Triangle OCF1 similar to Triangle F1A'B'
A'B'/OC=A'F1/OF1
OC=AB
A'B'/AB=A'F1/OF1=OF1-OA'/OF1
A'B'/AB=OF1-OA'/OF1---------------(2)

from eqn 1 and 2 we get
OA'/OA=OF1 - OA'/OF1
-v/-u= -f-(-v)/-f
v/u= f+v/f
-vf=-uf+uv

on dividing both sides by uvf we get
1/u=1/v+1/f
1/v-1/u=1/f


magnification m=height of image /height of object or m=v/u

Answer 2

Spherical lenses formed by binding two spherical surfaces bulging outward are known as convex lenses while the spherical lenses formed by binding two spherical surfaces such that they are curved inward are known as concave lenses. Images formed by these lenses can be real or virtual depending on their position from the lens and can have a different size too. The image distance can be calculated with the knowledge of object distance and focal length with the help of lens formula. It is an equation which relates the focal length, image distance and object distance for a spherical mirror. It is given as,
+ =
i= distance of image from the lens
o= distance of object from the lens
f= focal length of the lens
The lens formula is applicable to all situations with appropriate sign conventions. This lens formula is applicable to both concave and convex lens. If the equation shows a negative image distance, then the image is a virtual image on the same side of the lens as the object. If this equation shows a negative focal length, then the lens is a diverging lens rather than the converging lens. This equation is used to find image distance for either real or virtual image.
Calculating magnification with the help of lens formula:
Magnification of a lens is defined as the ratio of the height of image to the height of object. It is also given in terms of image distance and object distance. It is equal to the ratio of image distance to that of object distance.
Where, m= magnification
h = height of image
h = height of object
Power of lens
Power of a lens is the measure of degree of convergence or divergence of the light rays falling on it. The degree of convergence or divergence depends upon the focal length of the lens. Thus we define power of lens as the reciprocal of the focal length of the lens used. It is given as,
Where f is the focal length of the lens used. SI unit of power is Dioptre (D). The power of concave lens is negative while the power of the convex lens can be positive.
Stay tuned with BYJU’S to learn more about lens formula, magnification and power of lens.
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i
o
Concave lens
Convex lens
Combination of both the lenses
None of these