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.

When an object is placed at a distance of 25 cm from a mirror, the mag

1.	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.
Answer» We know that `m=-(v)/(u)=(f)/(f-u)` Here, `m_(1)=(f)/(f-(-25))=(f)/(f+25)` and `m_(2)=(f)/(f-(-25-15))=(f)/(f+40)` Since ` (m_(1))/(m_(2))=4, ` therefore `(f+40)/(f+25)=4` `f+40=4f+100` or `f=-20 cm` The negative sign shows that the mirror is concave.

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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.

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