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When an object is placed at a distance o...

When an object is placed at a distance of 25 cm from a mirror, the magnification is `m_(1)`. The object is moved 15cm farther away with respect to the earlier position, and the magnification becomes `m_(2)`. If `m_(1)//m_(2)=4` , then calculate the focal length of the mirror.

A

20 cm, convex

B

20 cm, concave

C

10 cm, convex

D

10 cm, concave

Text Solution

Verified by Experts

The correct Answer is:
B
As, `m = - (v)/(u) = (f)/(f - u)`
So, `m_(1) = (f)/(f-(-25)) = (f)/(f + 25)`
Simillariy, `m_(2) = (f)/(f+40)`
and `(m_(1))/(m_(2)) = 4`
`therefore (f + 40)/(f + 25) = 4`
f = - 20 cm
Negative sign shows that mirror is concave.
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