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As shown in the figure, a thin rod AB of...

As shown in the figure, a thin rod AB of length 10 cm is placed on the principal axis of a concave mirror such that it.s end B is at a distance of 40 cm from the mirror. If the focal length of the mirror is 20 cm, find the length of the image of the rod

Text Solution

Verified by Experts

`rArr` / = 20 cm and the end B is at distance 40 cm = 2f = R. Thus the image of B is formed at B only. Now for end A, u = - 50cm, f = - 20 cm, v=?
In `1/u + 1/v = 1/f,` putting these values
`- 1/50 + 1/v = - 1/20`
`therefore 1/v = 1/50 -1/20 = (20-50)/(20 xx 50) = - (30)/(1000)`
`therefore v = - (1000)/(30 = - 33.3 cm `
This image `Lambda` is on the same side as the object Now, length of the image = 40 - 33.3 = 6.70 cm
=0 .0670 m
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