object is placed at a distance of 60 cm from a convex mirror where is the magnification produced is 1 by 2 where should be the object is placed at the get magnification of 1 by 3
Answers
When an object is placed at a distance of 60cm from a convex spherical mirror, the magnification produced is 1/2. Where should the object placed to get magnification of 1/3?
The mirror formula is 1v+1u=1f, where,
u is the distance of the object from the mirror,
v is the distance of the image from the mirror, and,
f is the focal length.
The distance from the mirror to the left is taken as negative and the distance from the mirror to the right is taken as positive.
The magnification is =hiho=−vu, where,
hi is the height of the image, and,
ho is the height of the object.
The distance above the principal axis is taken as positive and the distance below the principal axis is taken as negative.
In a convex mirror, u is always negative and f is always positive.
In a convex mirror the image is always virtual and hence magnification is always positive.
It is given that u=−60 cm and magnification =12.
⇒−v−60=12.
⇒v=30.
⇒130−160=1f
⇒1f=160⇒f=60 cm.
In the second case, it is given that magnification =13.
⇒−vu=13⇒1v=−3u.
1v+1u=1f.
⇒−3u+1u=1f
⇒−2u=1f.
⇒u=−2f=−2×60=−120 cm.
⇒ To get a magnification of 12 the object should be kept at a distance of 120 cm from the mirror.
Given:
u=-60cm
m=1/2
m=-v/u
1/2=-v/-60
-v=-30cm
v=30cm
f=?
by mirror formula:
-1/60+1/30=1/f
on solving:
f=60cm
m=1/3
1/3=-v/u
v=(1/3)u
f=60cm
using mirror formula:
1/u+1/v=1/f
1/u-3/u=1/60
u=-120cm