4. An object is placed in front of a concave mirror of focal length 20 cm. The image formed is three times the size of the object. Calculate two possible distances of the object from the mirror.
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4. An object is placed in front of a concave mirror of focal length 20 cm. The image formed is three times the size of the object. Calculate two possible distances of the object from the mirror.
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Answer:
Okay, so,
Focal length= 20cm.
Radius of curvature= 2×focal length= 2×20=40cm.
Let object actual height be h.
Image height: 3h.
Let image be virtual.
Thus, magnification= 3.
Magnification= -v/u
3=-v/u
transpose u.
v=-3u..(1)
Now, mirror formula:
1/f=1/u+1/v............(2)
Substitute (1) in (2)
1/-20=1/u+1/3u
1/-20=2/3u
u=-13.3cm.
Therefore, using Magnification= -v/u, v=-3×-13.3
v=39.9cm.
Now, let image be real.
Thus, magnification= -3
Magnification= -v/u
-3=-v/u
transpose u.
v=3u..(3)
Now, mirror formula:
1/f=1/u+1/v.......(4)
Substitute (3) in (4)
1/-20=1/u+1/3u
1/-20=2/3u
u=-26.67cm.
Again, using Magnification= -v/u,
v=-26.67×3
v=-80.01cm.
THUS, TWO POSSIBLE DISTANCES ARE 39.9cm AND 80.01cm.
HOPE THIS HELPS :D