Question

Two objects A and B when placed one after another in front of a concave mirror of focal length 10 cm form images of same size. size of object A is 4 times that of B. if object A is placed at a distance of 50 cm from the mirror, what should be the distance of B from the mirror

Answer 1

Let the magnification of object A =mA

mA= height of image hi/height of object ho.

mA = hiA/hoA=f/f-uA ---- 1

mB=hiB/hoB=f/f-uB ------- 2

Now,1 and 2

mA/mB= hiA/hoA = hoB/hiB=f-uB/f-uA ------- 3

f=-10

uA=-50

hiA =hiB= hiA

hoA=4hoB

Putting values in equation 3 ,we get

hoB/4hoB=-10-4uB/-10-(-50)

1/4=-10-uB/-10+50

-40-4uB=40

40+40=-4uB

80=-4uB

80/-4=uB

-20=uB

So distance of object B from mirror is -20 cm.

Answer 2

Let the magnification of object A =mA

mA= height of image hi/height of object ho.

mA = hiA/hoA=f/f-uA ---- 1

mB=hiB/hoB=f/f-uB ------- 2

Now,1 and 2

mA/mB= hiA/hoA = hoB/hiB=f-uB/f-uA ------- 3

f=-10

uA=-50

hiA =hiB= hiA

hoA=4hoB

Putting values in equation 3 ,we get

hoB/4hoB=-10-4uB/-10-(-50)

1/4=-10-uB/-10+50

-40-4uB=40

40+40=-4uB

80=-4uB

80/-4=uB

-20=uB

So distance of object B from mirror is -20 cm.