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CBSE Class 10 Answered

how can we find the focal length of a mirror or lenses  
Asked by abhishekayush15 | 11 Nov, 2018, 10:17: AM
answered-by-expert Expert Answer
Focal length of concave mirror:-
 
As shown in fig.1 , parallel rays are getting focused at the focal point F of concave mirror. Hence object at a far point
from mirror is considered as object at infinite distance and its image is formed at focal point. Then we can measure the
focal length f beween pole P of the mirror and focal point F.

In an alternate method, an object is placed at the principle axis of mirror and its image is obtained. Let the distance between
pole P of mirror and object is u. Let the distance between pole P of mirror and image is v. Then using the mirror equation
(1/v)+(1/u) = (1/f), we get the focal length f.
 
Focal length of convex mirror:-
Initially an image I of an object O is formed using a convex lens as shown in figure 3. Position of image is marked.
Then without disturbing the position of lens and object the convex mirror is placed between image point and lens as shown in fig.4,
then the position of convex mirror is adjusted such that, now an image is formed side by side of object as shown in figure.Image is formed
side by side of object means, light rays are getting retraced after reflection from convex mirror. Hence light rays are normal to convex mirror.
At this position of the convex mirror, the distance between pole of the mirror and previous image point I is the radius of curvature of the mirror.
Then half of radius of curvature of the convex mirror is focal length of that mirror.
 
Focal length of convex lens:-
Parallel rays are getting converged at focal point of convex lens as shown in left side of figure 4.
Hence image of a far away object is formed using convex lens. Since a far away point object can be considered as an object
at infinite distance and the light rays are coming towards the convex lens are parallel, the imeage is formed at focal point.
By measuring the distance from optical centre to image point we can get the focal length of convex lens.

In an alternale way an object is placed at the principal axis of the lens and its image is obtained on the other side of lens.
Let u be the distance between optical centre of lens to object. Let v be the distance between optical centre of the lens to image.
Then from lens equation (1/v) - (1/u) = (1/f), we can get the focal length f of convex lens.
 
Focal length of concave lens:-
In order to find the focal length of concave lens it is combined with a convex lens of known focal length and
combination of this two lenses are used as shown in figure. Focal length of combination of lenses is obtained either using
parallel rays from a distant object or by using the lens equation as described before for convex lens.

If f1 is the focal length of convex lens and f2 is the focal length of concave lens, then the focal length F of combination is given by
(1/F) = (1/f1) + (1/f2) . Hence from known value of f1 and the measured value of F, we can find the focal length f2 of concave lens.
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