Lens Formula
Lens Formula
If we place an object at a distance u from the optical centre 'O' and its image is formed at a distance v then
This relationship is known as lens formula. Here f is the focal length of this lens.
Proof:
Consider an object AB placed beyond 2F in front of a convex lens. On the other side of lens an image is formed between F and 2F which is real, inverted and smaller in size. Applying the sign conventions :
Object distance (OB ):= -u
Image distance(OB') := v
Focal length(OF): = +f
In and
=
( vertically opposite angle)
=
( each
)
(By AA similarity)
Therefore, and
are equi-angular and hence they are similar.
............[ 1 ]
Now and
=
( vertically opposite angle)
=
( each
)
(By AA similarity)
Therefore, and
are equi-angular and hence they are similar.
In particular ,
But OC = AB
Since all distances are measured from optical centre , therefore,
...........[ 2 ]
Now comparing eq. (1) and (2),
Dividing both the sides by uvf,
Hence the Lens formula
Similarly we can prove the lens formula for a concave lens.
Illustration: An object is placed 30 cm from a convex lens. A real image is formed 20 cm from the lens. Find the focal length of the lens.
Solution: By convention, the object is placed to the left of the lens. Hence, u is negative. Since the image is real, the transmitted rays actually intersect. The image is thus formed on the right of the lens as shown in figure.
Hence, v is positive. Thus,
u = - 30 cm and v = + 20 cm.
From the lens equation we have,
or f = 12 cm.
Hence the focal length is 12 cm.
The focal length is positive for _______________ . | |||
| Right Option : B | |||
| View Explanation | |||
Which of the following are correct ? (a) The lens formula u stands for object distance . (b) The lens formula v stands for image distance . (c) The lens formula f stands for focal length. | |||
| Right Option : D | |||
| View Explanation | |||
In the lens f' stands for ._____________. | |||
| Right Option : A | |||
| View Explanation | |||
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