Question

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.​

Answer 1

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